
I mean, the fated pairs thing as a whole is kind of fucked up in itself, and it seems that this Rin guy is miserable af to begin with and came to believe that the only way for his life to get better is through some obligated romance...
For him to want that romance over all things is expected from this character, until he gets the idea out of his head, probably falling in love for Todoriki/Todoki??? guy.
He's desperate, confused and doesn't think things through, a tragedy really.

Well to say that you have to take into consideration the effect a fated pair has. Remember this is OMEGAVERSE FICTION so certain rules and regulations apply. He's desperate and doesn't think things through because in that world they simple can't do that when it comes to those things (as an unbonded Omega I suppose)
Their world is not the same as ours
Okay, the story itself is sad but this Rin guy just annoys the heck out of me. You don't know anything about each other, literally zero, and you demand that Yuka breaks their pair and lives the rest of his life in agony AND YET, doesn't take the freaking medicine? At this point Im not even surprised what's happening to him.