Frenemies: You're Not Who I Thought You Were

Another workable variation on frenemies is that the protagonists have misunderstood the essential character of the other.

In On and Off, Kang would remain irritated and uninterested in Ahn if Ahn truly was as conniving (I'll use any means, including my body, to get ahead) as Kang initially assumes. Sure, Ahn slept with Kang. But the relationship would never go anywhere if Kang thought he was dealing with a manipulator. 

A manipulative relationship CAN work. That is, a member of the couple can realize, "Wow, my lover is always playing games and looking for a personal benefit. Okay! I can handle that."

However, the manga On or Off establishes that Kang despises such behavior. He falls for Ahn when he realizes that Ahn was desperate to not let down his fellow "programming in a garage" freelancers. (And Kang feels guilty, though Ahn doesn't blame him.)

In fact, it takes a volume or two for Kang to figure out his youthful, impetuous lover. At the end of Volume 2, although he has begun to suspect that his original assessment was wrong, he still assumes Ahn will act coy and play a flirtatious game with him full of double-meaning. But, in fact, Ahn is entirely guileless. What he says is in fact what he means! 

Cherry Magic also begins with misapprehensions. Adachi assumes that Kurosawa is Mr. Handsome-Everything-Perfect Guy. He admires him, including how hard Kurosawa works. But he doesn't really begin to fall for him until he realizes that Kurosawa is kind of a mental mess and...mushy. 

It is Kurosawa's flaws that draw out Adachi's affection, not his perfections.