The Rapture is not biblical and was not taught by the apostles or their successors. The whole thing was simply made up whole cloth by members of a small sect called the Plymouth Brethren in the 1820s. (The Plymouth Brethren are still around, btw.)
Here's a short video to get up to speed on how it came to be: Where Did Rapture Theology Come From? by leading Bible scholar Ben Witherington.
And the long course, 32 minutes, by William Lane Craig: