I have always wondered if Jesus made an oblique reference to the Rapture during the Olivet Discourse in Mt. 24.28 and Luke 17:37. His statement about “where the body is, there the eagles gather” appears to be a direct reply to the disciples’ question about the whereabouts of the woman grinding grain who was taken (Lk 17.35). That verse’s parallel is ordered differently in Matthew (Mt 24.41), and no interjected question is mentioned, so the connection may be less apparent in Matthew. I have never been very satisfied with other explanations of Jesus’ remark about bodies and vultures, and I would like to think He was not totally silent about the Rapture in the Olivet context, even if He left it for Paul to tell us the mystery.
The Greek word for eagle is also translated vulture and the one for body also means a corpse. But why wouldn’t Jesus be silent about the rapture in the Olivet Discourse? It will have already happened. And besides, the Olivet Discourse was for Israel, and the context is the End of the Age and the 2nd Coming. Israel is not involved in the rapture.
In the desert you find the location of a carcass (body) by looking up into the sky for the vultures (eagles). It’s the only place they gather. The Lord’s context in Matt. 24:23-28 is looking for the Messiah. Following the vulture / carcass analogy Jesus was telling those who will be alive on Earth at the time to look up into the sky to find Him, not some place on Earth.
In Luke 17:34-37 the Lord was talking about Tribulation survivors, just like He was in Matt. 24:40-41, and He used the same Greek words, taken and left. The word translated taken means to receive to Himself, and the word for left means to put away. These words can only describe what happens at the 2nd Coming, so the disciples’ question “Where, Lord?” in verse 37 pertains to both groups. Believers will be received to Him and will enter the Kingdom. Unbelievers will be put away, taken off the planet. It’s a summary of the Sheep and Goat judgment, and does not describe the rapture. He was using the vulture / carcass analogy to say that each group will gathered in the place where they belong.