Klaine breaking up was a golden opportunity to give Blaine some much-needed character development and grow into more of an independent character instead of following Kurt around like a lovesick puppy dog.
Instead, they had him spend half the time wandering the halls crying and singing love ballads while flipping through scrapbooks of Kurt, in between getting a crush on his BFF Sam and singing a love song to him, which just made Blaine look even more wishy washy, and culminating in something as absurd as wanting to propose to his EX, which just made Blaine look desperate and ridiculous.
The whole thing just made Blaine look even more hopelessly surgically attached to Kurt than he was BEFORE they broke up.
As for Kurt, they gave short shrift to his entire perspective about the break-up by having Blaine moan about it to Sam and anyone else who would listen while never giving he and Kurt a single scene to substantially talk about it and the reasons why stuff happened (even when they had Kurt say he wanted to have a "mature heart-to-heart" over Christmas, and then the writers kind of just forgot about it), making their reunion not feel earned because neither of them addressed their own faults: Blaine's clingy levels of co-dependence and Kurt's selfishness, BOTH of which contributed to the break-up. But Kurt is never wrong, according to the writers, so we'll never have him acknowledge the fact that he's not the world's best boyfriend either.
The break-up was a perfect opportunity for them to both become more self-aware and grow as people, but the writers didn't do anything with it.