At the rapture, only those who are looking for him will see him:
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Hebrews 9:28 ESV
So Christ, having been offered once to bear the sins of many, will appear a second time, not to deal with sin but to save those who are eagerly waiting for him.
Now contrast that with the second coming to the earth
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Revelation 1:7
Behold, he cometh with clouds; and every eye shall see him, and they also which pierced him: and all kindreds of the earth shall wail because of him. Even so, Amen.
Hebrews 9:28 KJV -
"So Christ was once offered to bear the sins of many; and unto them that look for him shall he appear the second time without sin unto salvation."
To put it to you another way, the above passage here is talking about Christ appearing a second time without sin being imputed to him (like with his first appearance), but unto the purpose of salvation. For Christ's second appearance here is dealing with salvation and not judgment; Which perfectly fits the context of discussion in Hebrews chapter 9.
For the context of Hebrews 9 deals with Christ entering the Holy Place once and for all. For the description of the rites and sacrifices of the law were far inferior to the dignity and perfection of the sacrifice of Christ. For Christ is our mediator and redemption from sin; In other words, Christ is our salvation. Which is the topic of discussion mentioned in verse 28.
And here is the same passage in the ESV.
Hebrews 9:28 ESV -
"So Christ, having been offered once to bear the sins of many, will appear a second time, not to deal with sin but to save those who are eagerly waiting for him."
Which again says that Christ is appearing not to deal with sin but to SAVE those who are waiting for him.
Now, your probably thinking to yourself, how is that a problem, right? Is not Christ saving the elect at His Second Coming?
Well, at Christ's Second Coming, Jesus is not so much saving the elect from the events at Armageddon, but He is gathering them to fight there. Which means the saints taken up at Christ's Second Coming will be partaking in executing Christ's Judgment upon the Earth. Which is not really the same thing as Christ appearing so as to save His elect from something. How so?
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Luke 17:34-37
"I tell you, in that night there shall be two men in one bed; the one shall be taken, and the other shall be left. Two women shall be grinding together; the one shall be taken, and the other left. Two men shall be in the field; the one shall be taken, and the other left."
And they answered and said unto him,
"Where, Lord?"
And he said unto them,
"Wheresoever the body is, thither will the eagles be gathered together."
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Matthew 24:28
For wheresoever the carcase is, there will the eagles be gathered together.
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Revelation 19:17-18 and
Revelation 19:14
And I saw an angel standing in the sun; and he cried with a loud voice, saying
"To all the fowls that fly in the midst of heaven, Come and gather yourselves together unto the supper of the great God; That ye may eat the flesh of kings, and the flesh of captains, and the flesh of mighty men, and the flesh of horses, and of them that sit on them, and the flesh of all men, both free and bond, both small and great."
And the armies which were in heaven followed him upon white horses, clothed in fine linen, white and clean.
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Jude 1:14
Behold, the Lord cometh with ten thousands of his saints,
In other words, at the Second Coming of Christ, the elect (or the fowls or the eagles) will be gathered to battle those who remain on the Earth or gather to the supper of the Great God to eat the flesh of kings and the flesh of captains. This of course is speaking metaphorically. The saints are not going to really eat people, but they are going to defeat the wicked people of this world in the final battle with Christ.