There is much misunderstanding about particular statements made by Jesus when he compared the days of His return analogistically to how it was in the days of Noah and Lot. The verses in question are as follows:

No one knows about that day or hour, not even the angels in heaven, nor the Son, but only the Father. As it was in the days of Noah, so it will be at the coming of the Son of Man. For in the days before the flood, people were eating and drinking, marrying and giving in marriage, up to the day Noah entered the ark; and they knew nothing about what would happen until the flood came and took them all away. That is how it will be at the coming of the Son of Man. Two men will be in the field; one will be taken and the other left. Two women will be grinding with a hand mill; one will be taken and the other left. (Matthew 24:36-41)

"Just as it was in the days of Noah, so also will it be in the days of the Son of Man. People were eating, drinking, marrying and being given in marriage up to the day Noah entered the ark. Then the flood came and destroyed them all. "

"It was the same in the days of Lot. People were eating and drinking, buying and selling, planting and building. But the day Lot left Sodom, fire and sulfur rained down from heaven and destroyed them all. "

"It will be just like this on the day the Son of Man is revealed. On that day no one who is on the roof of his house, with his goods inside, should go down to get them. Likewise, no one in the field should go back for anything. Remember Lot's wife! Whoever tries to keep his life will lose it, and whoever loses his life will preserve it. I tell you, on that night two people will be in one bed; one will be taken and the other left. Two women will be grinding grain together; one will be taken and the other left." (Luke 17:26-35)

Jesus uses both the accounts of Noah and Lot to describe an event that is to occur on the day of His return. Specifically, some will be taken from Earth and others will remain on Earth.

The issue some theories have is deducing what is meant by (summarizing) "two will be together, one will be taken, one will be left", as used in the above verses. Many understand the one "to be taken" will be the believer - taken away from the Earth. However, is this what the Bible teaches?

Who will be Taken?

To understand the answer to this question, we need to read the accounts Jesus is quoting with respect to Noah and Lot. Underlining will be used to set focus of the answer:

So Lot went out and spoke to his sons-in-law, who were pledged to marry his daughters. He said, "Hurry and get out of this place, because the LORD is about to destroy the city!" But his sons-in-law thought he was joking. With the coming of dawn, the angels urged Lot, saying, "Hurry! Take your wife and your two daughters who are here, or you will be swept away when the city is punished." When he hesitated, the men grasped his hand and the hands of his wife and of his two daughters and led them safely out of the city, for the LORD was merciful to them. (Genesis 19:14-16)

Everything on dry land that had the breath of life in its nostrils died. Every living thing on the face of the earth was wiped out; men and animals and the creatures that move along the ground and the birds of the air were wiped from the earth. Only Noah was left, and those with him in the ark. (Genesis 7:22-23)

In both accounts, it is clear.

The one "left" is the object of God's desire .. Noah and Lot.

Those who were "taken away" were those who were the objects of God's wrath.

Such will be the case when Jesus returns:

Another angel came out of the temple in heaven, and he too had a sharp sickle. Still another angel, who had charge of the fire, came from the altar and called in a loud voice to him who had the sharp sickle, "Take your sharp sickle and gather the clusters of grapes from the earth's vine, because its grapes are ripe." The angel swung his sickle on the earth, gathered its grapes and threw them into the great winepress of God's wrath. They were trampled in the winepress outside the city, and blood flowed out of the press, rising as high as the horses' bridles for a distance of 1,600 stadia (Revelation 14:17-20)

but on the day that Lot went out from Sodom it rained fire and brimstone from heaven and destroyed them all. "It will be just the same on the day that the Son of Man is revealed. (Luke 17:29-30)

For as in those days before the flood they were eating and drinking, marrying and giving in marriage, until the day that Noah entered the ark, and they did not understand until the flood came and took them all away; so will the coming of the Son of Man be. (Matthew 24:38-39)

Jesus is very clear in Matthew 24:39 - "the flood came and took them all away".

Whoever is "left" ("remains") will be a survivor on Earth on the day of Jesus' return to be with the Lord forever.

Whoever is taken, will be swept away, destroyed, thrown into the winepress of God's wrath.