Taeui is so funny because in the third book, a potential second ml was badmouthing ilay and this is how it went:

Second ml: find a decent guy instead of that psychopath.

Taeui: what do you know about ilay?? I'll have you know that he has a lot of merits
(please don't ask me about those merits)

Second ml: .....what merits? 

Taeui: (FU** I TOLD YOU NOT TO ASK!!)

This Ml is actually trash, even after he finds out Mc's identity, he never apologizes.

I read it a while ago so He didn't cheat, from what I remember it was his cousin but he didn't try to explain anything to mc in person. There was someone who texted ml from mc's phone stating that he didn't want anything to do with ml. 
honestly, I still don't like ML's attitude. Even if my partner seems secure, I should still explain or debunk rumors,  unfounded or not. All he does is act like nothing is wrong without actually fixing anything. Because what do you mean, you left him alone for 10 years and now out of nowhere are acting jealous???