ITS simple brother
Paul didn't thesalonians confused, think the rapture already happen.
"[purporting] that the Rapture IS PRESENT [PERFECT indicative - G1764 Strong's Greek: 1764. ἐνίστημι (enistémi) -- to place in, to be at hand, perf. part. to be present (biblehub.com) ]"...
...they were under NO SUCH DELUSION!!
Instead, the actual wording (as your original post was worded), "[purporting] that THE DAY OF THE LORD IS PRESENT [PERFECT indicative - G1764]]"
"The Day of the Lord" is "an EARTHLY-located-TIME-PERIOD-[of much duration]-involving-JUDGMENTs-unfolding-upon-the-earth, followed-by-a-period-of-time-of-BLESSINGs" (NOT "a singular 24-hr day"), which STARTS [/ARRIVES] at the INITIAL "birth PANG [SINGULAR; 1Th5:2-3; Matt24:4/Mk13:5]" that Jesus spoke of in His Olivet Discourse (where "the beginning of birth PANGS [PLURAL]" is EQUIVALENT to the "SEALS" of Rev6 at the START of the trib... THAT is the ARRIVAL of "the DOTL TIME-PERIOD" to play out upon the earth, over TIME).
The "definition" of that phrase is NOT "Rapture". ["Rapture [IN THE AIR]"]
No one was "[purporting] that the RAPTURE *is present [perfect indicative - G1764]*" (your incorrect interp of v.2).
Than Paul say, that day Will not happen before the antichrist Being reveal.
"that day [the DOTL from v.2!] will not be present if not shall have come THE DEPARTURE *FIRST* and [distinctly] the man of sin be revealed..."
notice... ONE THING *FIRST* (not BOTH of those things FIRST), which distinguishes them.
Once "the man of sin" is REVEALED, the "DOTL" WILL BE PRESENT (to unfold upon the earth; JUDGMENTs unfolding upon the earth over the course of SOME TIME... "IN HIS TIME" [re: "the man of sin" and ALL he will DO over the course of THOSE SEVEN YEARS])
And we know antichrist reveal during second part of gt.
So rapture after gt.
What WAS "persuasive" (to what they were ACTUALLY being told by false-conveyors) was "that THE DAY OF THE LORD *IS PRESENT* [PERFECT indicative]": an EARTHLY time-period consisting of JUDGMENTs unfolding upon the earth OVER THE COURSE of some TIME.
THAT would be EASY (and would be PERFECTLY REASONABLE) for them to be [wrongly] persuaded to believe, BECAUSE of the VERY NEGATIVE THINGS they were presently and ONGOINGLY *experiencing* (per 2Th1:4).
The other makes no sense whatsoever. ZERO PEOPLE had DISAPPEARED!
The text does not SAY what you are having it to say.
[study all that the OT has to say about "the DOTL"--it is not a mere "singular 24-hr day" nor does it COMMENCE at the moment of Christ's "RETURN," but quite a bit EARLIER THAN THAT ]