I wonder if the fact Yuu decided to confess to every Karin was interpreted as "You like all of them, huh? Then you don't really like any of them. You just didn't want to have to choose what part you liked" in some weird roundabout way.
I did think early know that just loving every part of her is somewhat wrong, they have their flaws, Karin wants to be better.
As an example if an alcoholic got his personality split, you wouldn't say that his drunken side was something that need to be kept right?
Karin like Yuu is a teenager, they have to grow and improve.
Karin should lose her arrogant/possessive/tsundere side.