Not true.
Your statement does not take into consideration the actual phrase (and specific wording) used, where it says,
"caught up TOGETHER WITH them"
Consider [quoting from BibleHub], regarding the word translated
"together" (in kjv), "G260 hama" -
"In
1 Thessalonians 4:17 and
1 Thessalonians 5:10, where
ἅμα is followed by σύν,
ἅμα is an adverb (
at the same time)
and must be joined to the verb."
[end quoting]
so, "caught up [<--that's the verb] together [<--that's connected to that verb; the verb-action is CONNECTED with this word] with [G4862 - a word denoting 'union' and/or 'identification'] them..."
This means they ("the dead in Christ" [who shall rise (be resurrected) first] AND the "we which are alive and remain unto") are "caught up" (like PAUL, a SINGULAR person) TOGETHER... AS
ONE BODY!
(this is the EVENT known as our Rapture; it will occur at a particular future point in time--one point in time)
In fact, Paul distinguishes what happens at our death, and what happens at our Rapture, in 2Cor5:1-8!