What you have just stated God does for every human being. That is why He is not a respector of persons. He desires that all of His creatures, who bear His Image, come to know Him and be joined with Him in a mutual relationship of love and obedience. God created man such that man has a natural link or search for God. Even in his fallen condition, man seeks, but the problem in his fallen state it becomes easy to direct that seeking incorrectly. Man then begins to worship the creation instead of the creator.
You are misusing Rom 3:11. Paul is making a point that has very little to do relative to the source of that statement which is Ps 14. As a contrast you should also read Ps 15 & 16.
No sir, I only quoted that one verse so I would make a quick point. I encourage you to read all of Romans 3. Because of man's fallen state everyone is under sin, thus man is dead in it (Ephesians 2:1-7). If man is dead, he cannot even attempt to find God, simply because he is dead! In Ephesians 2:1-7, it's clear that God must make us alive together with Christ. Continuing from those verses, it says that we are saved by grace through faith that not of yourself it is a gift of God; faith is a gift of God, not a product of man. God must first give man faith for him to believe the gospel.
We see in John 1:12-13, we have the gift of adoption as children of God who received Christ, but we are born again by the will of God alone, not by the will of the flesh or the will of man. If you couldn't choose to be born the first time, what makes you think you can the second? John 1-12-13 is clear on this. Same goes for John 3:3-8, a man cannot see the kingdom unless he is born again (v. 3), he cannot enter it either unless he is born again (v. 5). In context, verse 8 gives a summary that it is not from man who becomes born again. So if a man could choose God by choice, he would be the reason for his spiritual birth, that's not what scripture is showing.
Regeneration --> Faith --> Salvation --> Sanctification = Work of the Spirit, by His grace.
There is no text in scripture that even hints that God preselects, elects anyone to salvation. He did not even do that with Adam, why would He do it for some privileged few, and consign the rest of humanity to destruction.
Man is also not totally depraved as understood by the Reformed view. God has redeemed all of mankind, given life to the world, and the Holy Spirit is actively calling all men to repentance.
Read Romans 9, that's a good place to start. You can read after that Ephesians 1:3-12, amazing is His divine will and purpose, and amazing is His amazing grace, how sweet the sound! I don't want to stress it too much, or else I would give you as many scriptures as I can find.
Another aspect of the Reformed view is Limited Atonement. If Christ's atonement was limited then Christ accomplished absolutely nothing. He did not overcome death for all. His death did not accomplish a completed sacrifice. The theology presents Christ as just another good man, an historical figure.
This is not right conception of it. Matter of fact, it can be a confusing one. God sent His Son to die for man's sins, it's main purpose is to redeem the lost elect in the world and bring them to Christ, to save His people from their sins (Matt. 1:21; John 10:15; Isaiah 53:8, etc). Repentance is a call for everyone, and whoever believes in Christ has a chance to be saved. But as we see here, only the elect happen to believe... (Matt. 22:1-14)
Christ's sacrifice is sufficient for all, but it's atonement is for the ones who believe (John 3:16). This is why it's limited, because if it were unlimited to everyone then everyone is saved, this is a false teaching of universalism. So in some way, even if you disagree with reformed theology, the concept of atonement is limited no matter what.
Irresistable grace is an affront to most of scripture because it is quite clear that beleivers still sin. They can reject Christ, can quench the Holy Spirit, can spurn their first faith. Which also denies the idea of perseverance of the saints.
God created man free so that man could freely love and obey Him. Man was redeemed, restored to life, to an eternal existence, so that God could call all men. God has given every man all the gifts necessary for His salvation, but man is free and the choice of life or death is all of man. God will hold all men accountable for their choices and actions. None can blame God for their judgement.
Another misconception. Irresistible grace does not mean God's grace can't be resisted. It means God will overcome the resistance. The bible teaches that the Holy Spirit never fails to bring salvation to the sinners whom He personally calls (John 6:37-40).
Perseverance of the saints is eternal security. If the scriptures say Jesus is the Author and Perfecter of our faith (Hebrews 12:2), then it's up to Him as to who will persevere in the end. If you weren't saved by works, then you cannot be lost by it either. If you could, then that would mean you earned your salvation and have had it taken away for not keeping up with it. Scripture is clear that we are saved by grace, and by grace we shall persevere (Phill. 1:6)
Again, saying God elects certain people does not mean we don't have choices. God can be 100% sovereign while we are also morally responsible. Free will is not the same thing as moral choices. Free will teaches that you can choose God outside of your natural state without God's full help. If that were true, then you would have something to boast about.
Can a man walk across a bridge? Yes, by his nature he is able to. Can a man fly over the bridge? No, because that's not in his nature. This is the same thing with a man who is totally depraved in the nature of his sin. He can make choices, but he cannot do them beyond his nature. God must make him a new creature with a new nature for him to choose God.