One thing to note about this pre-tribulation Rapture is that it has Jesus coming not twice, but three times. Now, Catholics and some Protestant groups (Lutherans, for example) also look forward to the Second Coming, when Christ will return to judge heaven and earth. At that time believers who are still alive will be caught up with Christ (we call it the Parousia). But the “Rapture”, as understood by some Protestants (and illustrated by the “Left Behind” book series) has Christ coming a second time to snatch up the “True Christians” (hint: they’re not Catholics) thus sparing them from the Tribulation, and then a third time for the Final Judgement. Now, they will deny this by saying that the Rapture represents a secret coming, but the Bible passages they use to back up their theory speaks of trumpet blasts, etc. Hardly secret. Also, if saving believers from tribulation were such a desirable thing to do, why have there been so many Christian martyrs who have suffered and died for Christ? I think this fear of Tribulation as something to be avoided is natural enough, but it’s going too far to construct a theology that has the True Christians escaping. We’re supposed to endure trials and tribulations for our faith, not get off scott-free 'cause we’re so darn nice.
As someone else has said, this theory goes back only to the 1830s.