I'm glad you asked this question. It proves that predestination, as Calvinists understand it, is Biblical.
Why?
Because no one would ask your question of you when you explained your view of predestination. But Paul, after explaining his view of predestination, expected people to ask him the question you asked:
"Thou wilt say then unto me, Why doth he yet find fault? For who hath resisted his will?" (Romans 9:19)
We Calvinists are in good company. We get the exact same objections that Paul, inspired the Holy Spirit, anticipated that he would get.
Remember this: you can know you're teaching Pauline doctrines when you're getting the same objections Paul anticipated. We know we're right about salvation by free grace through faith alone when people say, "Shall we continue in sin, that grace may abound?" (Rom. 6:1) Likewise, we know we're right about predestination when people say, "Why are we still responsible for our sins if God is sovereign like you say?"
And I'm glad that you gave this answer because it further documents just how terribly wrong you actually are. First of all, for the life of me, I cannot even imagine why you'd even seek to compare your beliefs to Paul's beliefs when Paul said earlier on in this epistle:
"And thinkest thou this, O man, that judgest them which do such things, and doest the same, that thou shalt escape the judgment of God? Or despisest thou the riches of his goodness and forbearance and longsuffering; not knowing that the goodness of God leadeth thee to repentance? But after thy hardness and impenitent heart treasurest up unto thyself wrath against the day of wrath and revelation of the righteous judgment of God; Who will render to every man according to his deeds: To them who by patient continuance in well doing seek for glory and honour and immortality, eternal life: But unto them that are contentious, and do not obey the truth, but obey unrighteousness, indignation and wrath, Tribulation and anguish, upon every soul of man that doeth evil, of the Jew first, and also of the Gentile; But glory, honour, and peace, to every man that worketh good, to the Jew first, and also to the Gentile: For there is no respect of persons with God." (Romans 2:3-11)
You don't believe any of that and especially not the last verse. Whereas Paul said that "there is no respect of persons with God", your "god" is very much a respecter of persons and your beliefs are therefore anti-Pauline in nature right from the start. Furthermore, cherry-picking isolated verses from Romans chapter 9 isn't going to help you when you're engaged in discussions with those who have not only read the entire chapter multiple times, but the entire epistle multiple times as well. For now, I'll just stick with chapter 9:
"I say the truth in Christ, I lie not, my conscience also bearing me witness in the Holy Ghost, That I have great heaviness and continual sorrow in my heart. For I could wish that myself were accursed from Christ for my brethren, my kinsmen according to the flesh: Who are Israelites; to whom pertaineth the adoption, and the glory, and the covenants, and the giving of the law, and the service of God, and the promises; Whose are the fathers, and of whom as concerning the flesh Christ came, who is over all, God blessed for ever. Amen. Not as though the word of God hath taken none effect. For they are not all Israel, which are of Israel: Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called. That is, They which are the children of the flesh, these are not the children of God: but the children of the promise are counted for the seed. For this is the word of promise, At this time will I come, and Sara shall have a son." (Romans 9:1-9)
Paul began this chapter (not that there were chapters and verses back then) by addressing Israel and by demonstrating that "they are not all Israel which are of Israel" and "neither because they are Abraham's seed are they all children" even as he did in his other epistles and Galatians, especially. IOW, there is a clear distinction being made between natural Israel and what Paul called "the Israel of God" (Galatians 6:16) and Abraham's natural descendants and those who truly comprise being a part of Abraham's seed as Paul described elsewhere (Galatians 3:26-29). Why did Paul do this? Again, he had basically been spending the entirety of his epistle up until this point by cutting off every possible natural means by which anybody might consider themselves to be a part of God's family and by continually showing them that there's no means of salvation apart from or outside of Christ. He had previously shown how natural outward circumcision avails nothing in chapter 2 and that an inward spiritual circumcision was required instead. He had already shown in chapters 2 & 3 that just being recipients of God's law means nothing and that the law actually condemns the whole world, both Jew and Gentile alike, in that there is no difference for all have sinned and fallen short of the glory of God. He then, of course, showed how both the law and prophets point to Christ as the only possible means of salvation. He jumped back to the topic of outward circumcision in chapter 4 and showed that Abraham had already had righteousness imputed unto himself via faith in Christ long before he was ever outwardly circumcised and how that Abraham is the father of all them that believe or the father of all of them who similarly place their saving faith in Christ. In chapter 5, he showed how through one man's (Adam's) disobedience all came under condemnation and how through one man's (Christ's) obedience all can be justified. He then explained the differences between the law of sin and death with its accompanying outward circumcision and the law of the Spirit of life in Christ Jesus with its accompanying inward circumcision in chapters 6 through 8. IOW, again, he'd been making a clear distinction between everything outward and natural and everything inward and supernatural or spiritual and he was still doing the same here in chapter 9. With this background, let's continue:
"And not only this; but when Rebecca also had conceived by one, even by our father Isaac; (For the children being not yet born, neither having done any good or evil, that the purpose of God according to election might stand, not of works, but of him that calleth); It was said unto her, The elder shall serve the younger. As it is written, Jacob have I loved, but Esau have I hated." (Romans 9:10-13)
I've already rather thoroughly addressed this portion of scripture here...
http://christianchat.com/bible-discussion-forum/119866-we-really-predestined-2.html#post2227730
...so I'll simply say that Paul was here cutting off the natural avenue of inheritance by birthright as the firstborn. IOW, although Esau was the firstborn, his descendants, the Edomites, served the younger or served Jacob's descendants, the Israelites. Anyhow, the point is that one's natural birthright counts for nothing in relation to salvation and Esau sold his birthright anyway. Yes, as Paul had just finished mentioning, our birthright is found in being conformed unto the image of Jesus, the FIRSTBORN among many brethren (Romans 8:29). Continuing on, we read:
"What shall we say then? Is there unrighteousness with God? God forbid. For he saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion. So then it is not of him that willeth, nor of him that runneth, but of God that sheweth mercy. For the scripture saith unto Pharaoh, Even for this same purpose have I raised thee up, that I might shew my power in thee, and that my name might be declared throughout all the earth. Therefore hath he mercy on whom he will have mercy, and whom he will he hardeneth." (Romans 9:14-18)
First of all, why did Paul ask, "What shall we say then? Is there unrighteousness with God?" Of course, there isn't. Again, God is totally righteous to only impute righteousness unto people via faith in Christ and such things as outward circumcision, being recipients of the law, being natural born Israelites, being natural descendants of Abraham and being the natural firstborn mean absolutely nothing in relation to God's imputed righteousness.
Secondly, where did God say what Paul cited to Moses? Well, he said it here:
"And he said, I beseech thee, shew me thy glory. And he said, I will make all my goodness pass before thee, and I will proclaim the name of the LORD before thee; and will be gracious to whom I will be gracious, and will shew mercy on whom I will shew mercy." (Exodus 33:18-19)
Okay, then to whom will God actually show mercy? Well, God went on to give us the answer to this most important question when He actually passed before Moses and showed him His glory:
"And the LORD passed by before him, and proclaimed, The LORD, The LORD God, merciful and gracious, longsuffering, and abundant in goodness and truth, Keeping mercy for thousands, forgiving iniquity and transgression and sin, and that will by no means clear the guilty; visiting the iniquity of the fathers upon the children, and upon the children's children, unto the third and to the fourth generation." (Exodus 34:6-7)
What God said here wasn't a new revelation because he had previously said to Moses and to all the children of Israel gathered around Mt. Sinai:
"And God spake all these words, saying, I am the LORD thy God, which have brought thee out of the land of Egypt, out of the house of bondage. Thou shalt have no other gods before me. Thou shalt not make unto thee any graven image, or any likeness of any thing that is in heaven above, or that is in the earth beneath, or that is in the water under the earth: Thou shalt not bow down thyself to them, nor serve them: for I the LORD thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me; And shewing mercy unto thousands of them that love me, and keep my commandments." (Exodus 20:1-6)
God expects us to have no other gods before Him and He shows mercy unto thousands of them that love Him and keep His commandments. What does any of this have to do with "predestination"? Nothing, of course. God has mercy upon those who choose to love Him and He further hardens those who choose to hate Him and that brings us to Paul's other Old Testament citation:
"And the LORD hardened the heart of Pharaoh, and he hearkened not unto them; as the LORD had spoken unto Moses. And the LORD said unto Moses, Rise up early in the morning, and stand before Pharaoh, and say unto him, Thus saith the LORD God of the Hebrews, Let my people go, that they may serve me. For I will at this time send all my plagues upon thine heart, and upon thy servants, and upon thy people; that thou mayest know that there is none like me in all the earth. For now I will stretch out my hand, that I may smite thee and thy people with pestilence; and thou shalt be cut off from the earth. And in very deed for this cause have I raised thee up, for to shew in thee my power; and that my name may be declared throughout all the earth. As yet exaltest thou thyself against my people, that thou wilt not let them go?" (Exodus 9:12-17)
What? The LORD hardened Pharaoh's heart? Yes, and...? Again, there are other places where we read that Pharaoh hardened his heart. Like here, for example:
"And Pharaoh hardened his heart at this time also, neither would he let the people go." (Exodus 8:32)
God knew that Pharaoh was wicked and that he would never repent and yet God deliberately chose to raise Pharaoh up to a place of prominence that He still might be glorified through Pharaoh's life by destroying him and his armies as He liberated the Israelites from cruel Egyptian bondage and this is all that Paul was addressing here as we'll now see:
"Thou wilt say then unto me, Why doth he yet find fault? For who hath resisted his will? Nay but, O man, who art thou that repliest against God? Shall the thing formed say to him that formed it, Why hast thou made me thus? Hath not the potter power over the clay, of the same lump to make one vessel unto honour, and another unto dishonor? What if God, willing to shew his wrath, and to make his power known, endured with much longsuffering the vessels of wrath fitted to destruction: And that he might make known the riches of his glory on the vessels of mercy, which he had afore prepared unto glory, Even us, whom he hath called, not of the Jews only, but also of the Gentiles?" (Romans 9:19-24)
I've already shown that God, the Potter, is more than capable to refashion the clay, any of us, when we repent...
"The word which came to Jeremiah from the LORD, saying, Arise, and go down to the potter's house, and there I will cause thee to hear my words. Then I went down to the potter's house, and, behold, he wrought a work on the wheels. And the vessel that he made of clay was marred in the hand of the potter: so he made it again another vessel, as seemed good to the potter to make it. Then the word of the LORD came to me, saying, O house of Israel, cannot I do with you as this potter? saith the LORD. Behold, as the clay is in the potter's hand, so are ye in mine hand, O house of Israel. At what instant I shall speak concerning a nation, and concerning a kingdom, to pluck up, and to pull down, and to destroy it; If that nation, against whom I have pronounced, turn from their evil, I will repent of the evil that I thought to do unto them." (Jeremiah 18:1-8)
...so why would you have us to believe that God creates men a certain way and that there is then no hope ever for actual change? Like I said, you don't know what you're talking about. All that Paul was saying here was that God suffered long in relation to Pharaoh and deliberately raised him up to a place of prominence that He might make a public display of His wrath upon somebody who never had any intention whatsoever of repenting and that He also might make His power known. IOW, God got glory out of Pharoah's life even though Pharaoh wanted nothing at all to do with God.
That's about it, folks. Not a word about anybody allegedly being "predestined" to eternal damnation and plenty of words, a whole epistle full, which declare that salvation is found in None other than Christ and that God's mercy is available unto all who call upon His name.