Did you notice in the context who was taken away (in Matthew 24:37-42)? It was not Noah and his family that were “taken.” Speaking of the wicked, verse 39 says “and did not know until the flood came and took them all away.” The wicked were taken away. Noah remained. This is the complete opposite of the modern rapture theory.
The context of “one will be taken and the other left” is “as the days of Noah were, so also will the coming of the Son of Man be.” The rapture will be like Noah’s time. Did Noah mysteriously disappear? When Noah entered the ark, did the world continue with normal daily life? We all know better. “The world that then existed perished” (2 Peter 3:6).
Jesus did not have the modern rapture doctrine in mind. Rather, He said that when He returns, the earth will pass away.
If the popular rapture theory were correct, Jesus would have used totally different examples. Jesus would have said, “As the days of Enoch were,” “as the days of Elijah were.” Righteous Enoch disappeared out of this world and the world continued on. Elijah’s case is even more striking. After the whirlwind took him up into heaven, 50 men went searching for him for 3 days. Now there is the flavor of today’s rapture doctrine!