@imtaciturn
I don't recall if it's been explained in the manga or the notes, but two possible explanations:
1.
Square peg in a round hole, an expression of forcing yourself or someone else to conform to an ill-fitting role.
2.
Squaring the circle, an ancient math puzzle that is proven to be impossible
with the restrictions of a compass+straightedge only.
(Emphasis added because many people leave this important tidbit out, leading to idiots and fools claiming so-called "solutions" which violate the restrictions.)
Definition one would obviously describe FMC's predicament quite well, and even the male lead to a certain extent as he realizes his feelings.
Definition two, meaning "literally impossible", would describe the male lead's (initial) assessment of him falling in love with FMC.
It is unlikely to be referring to a literally round-the-corner rounded-corner square, known as a
squircle.