Would, "the taken," or, "the left," of Matthew equate to; that we who are alive and remain until the coming of the Lord will by no means precede those who are asleep. of 1 Thes 4:15
Where are they preceding to?
No, the taken and left are those who are alive when the Lord Returns.
While in Matthew there is just a small mention of the eagles gathering...
Matthew 24:27-28
King James Version (KJV)
27 For as the lightning cometh out of the east, and shineth even unto the west; so shall also the coming of the Son of man be.
28 For wheresoever the carcase is, there will the eagles be gathered together.
...we see in Luke a little more detail given, and we can pick up the context early to see that in view is the same event described in Matthew 24:
Luke 17:22-27
King James Version (KJV)
22 And he said unto the disciples, The days will come, when ye shall desire to see one of the days of the Son of man, and ye shall not see it.
23 And they shall say to you, See here; or, see there: go not after them, nor follow them.
24 For as the lightning, that lighteneth out of the one part under heaven, shineth unto the other part under heaven; so shall also the Son of man be in his day.
25 But first must he suffer many things, and be rejected of this generation.
26 And as it was in the days of Noe, so shall it be also in the days of the Son of man.
27 They did eat, they drank, they married wives, they were given in marriage, until the day that Noah entered into the ark, and the flood came, and destroyed them all.
So we can safely conclude that the context remains that which is the theme of both chapters, which that of the Lord's Return. We see that His Return involves judgment, and that is here likened to the judgment visited on those in Noah's day.
To make it clear to His students the Lord again gives an example of judgment...
28 Likewise also as it was in the days of Lot; they did eat, they drank, they bought, they sold, they planted, they builded;
29 But the same day that Lot went out of Sodom it rained fire and brimstone from heaven, and destroyed them all.
30 Even thus shall it be in the day when the Son of man is revealed.
...and we see again it is the same context, the Lord's Return. And a primary thrust of this teaching is "When I return there will be judgment like there was in those two examples."
31 In that day, he which shall be upon the housetop, and his stuff in the house, let him not come down to take it away: and he that is in the field, let him likewise not return back.
32 Remember Lot's wife.
I take this to mean "Do what I tell you." Wife disobeyed the directive of God and was herself included in the judgment she should have escaped. Disobedience is often connected with unbelief, and that unbelievers are in view is made clear in Matthew 25.
33 Whosoever shall seek to save his life shall lose it; and whosoever shall lose his life shall preserve it.
Here it is made clear that physical death is involved in this judgment.
34 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.
35 Two women shall be grinding together; the one shall be taken, and the other left.
36 Two men shall be in the field; the one shall be taken, and the other left.
Now here is where we see His terms defined:
37 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.
The disciples are asking "Where are they taken?" I guess we could try to make it say "Where are they left," but taken seems to fit better, I think.
Regardless, what we can say is that His primary thrust is one of judgment, and whether it refers to taken or left, the end result is physical death. That is what happened in the examples, and that is why He uses them. It is not until we get to Matthew 25 that we see that in the Judgment of the Sheep and Goats, it is the believers who are "left" alive, while the unbelievers are taken in judgment and their death is described as entrance to eternal punishment.
Christ taught, in regards to the Millennial Kingdom, that nothing that offends will enter that Kingdom, and that only those born again would.
We see this imagery in the Old Testament:
Ezekiel 39
King James Version (KJV)
39 Therefore, thou son of man, prophesy against Gog, and say, Thus saith the Lord God; Behold, I am against thee, O Gog, the chief prince of Meshech and Tubal:
2 And I will turn thee back, and leave but the sixth part of thee, and will cause thee to come up from the north parts, and will bring thee upon the mountains of Israel:
3 And I will smite thy bow out of thy left hand, and will cause thine arrows to fall out of thy right hand.
4 Thou shalt fall upon the mountains of Israel, thou, and all thy bands, and the people that is with thee: I will give thee unto the ravenous birds of every sort, and to the beasts of the field to be devoured.
5 Thou shalt fall upon the open field: for I have spoken it, saith the Lord God.
We see it in the New Testament:
Revelation 19:17-21
King James Version (KJV)
17 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;
18 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.
19 And I saw the beast, and the kings of the earth, and their armies, gathered together to make war against him that sat on the horse, and against his army.
20 And the beast was taken, and with him the false prophet that wrought miracles before him, with which he deceived them that had received the mark of the beast, and them that worshipped his image. These both were cast alive into a lake of fire burning with brimstone.
21 And the remnant were slain with the sword of him that sat upon the horse, which sword proceeded out of his mouth: and all the fowls were filled with their flesh.
This shows the consistency of Prophecy and Christ's teaching. We have the enemies of God slain which corresponds to Christ's teaching about judgment when He returns, and those who are left enter into that Kingdom:
Matthew 25:31-34 & 41
King James Version (KJV)
31 When the Son of man shall come in his glory, and all the holy angels with him, then shall he sit upon the throne of his glory:
32 And before him shall be gathered all nations: and he shall separate them one from another, as a shepherd divideth his sheep from the goats:
33 And he shall set the sheep on his right hand, but the goats on the left.
34 Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world:
41 Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:
We would not really consider those that remain alive to be "taken." And we look at this and consider that these Sheep are not glorified, but rather than being destroyed physically, they are spared, which leaves them in their current state, which is like unto ours today: physical and born again.
The singular problem, as mentioned before, for the Post-Tribulation view is that if the Rapture occurs at Christ's Return, then we have a few problems to reconcile.
The first would be that this does not depict a Rapture, but simply the gathering prophesied in the Old Testament.
Secondly, Paul does not include unbelievers in his Rapture teachings.
Third, Revelation 20 excludes the Rapture of the Church because only Tribulation Martyrs are mentioned, and nothing about those still living is mentioned.
Fourth, it conflicts with Christ's teaching such as we have just looked at.
Fifth, and finally (for now), this scenario leaves no physical believers who will have offspring that rebel against God when Satan is released from his imprisonment:
Revelation 20:7-9
King James Version (KJV)
7 And when the thousand years are expired, Satan shall be loosed out of his prison,
8 And shall go out to deceive the nations which are in the four quarters of the earth, Gog, and Magog, to gather them together to battle: the number of whom is as the sand of the sea.
9 And they went up on the breadth of the earth, and compassed the camp of the saints about, and the beloved city: and fire came down from God out of heaven, and devoured them.
The only possible way this multitude of rebels could come about is if there are physical descendants of the born again believers who are the Sheep of Matthew 25. Paul taught that the Rapture of the Church would include both those who are living as well as those who are dead, and they are all glorified at this time. We would have to get into some serious speculative ideas to reconcile these problems, but...
...we need not do that.
The Pre-Tribulational Rapture is the only view that can be reconciled without negating other teachings, as all groups who have embraced another view are forced to do. They leave Scripture in a shambles because they have to remove a great many prophecies and promises of God in order to make their system work.
God bless.