
I think it was shown since the beginning.
When he talked to his sister about that actor marrying the younger girl, when he was thinking about Yeroum's academic situation, at the park/concert. Mr Lim had most of the time present the age gap in a way or another
This is not about insecurity is about act like the adult cause YOU ARE the adult
16 years is a huge gap specially considering Yeroum's in his 20s

100% it was beyond jarring seeing him be so unkind. The idea that that would be the "only way Yeorum would give up" is only true in melodrama and it was disappointing to see a 40 year old character who until now was portrayed as thoughtful and caring acting like a character out of some toxic teen romance.
Listen, I get that Mr. Lim is still very insecure and concerned about his relationship with Yeoreum, especially after talking with his aunt, but this kind of cruelty feels so forced and out of character. Acting so cold toward Yeoreum and breaking off a relationship you were JUST ready to dive into just feels like a really cheap way of creating another conflict without really taking into account the journey these characters have taken thus far. I would've appreciated it more if they actually had Mr. Lim and Yeoreum become an official couple and navigate a more realistic conflict that the two would face, such as their family's or coworker's reaction to their new relationship, how they navigate through that shame and turmoil, and let their love prevail. I'm sure the author will eventually be able to pull this arc off regardless, I just don't appreciate how it sort of shifts Mr. Lim's character into something that was never shown or indicated prior to the convenience of this current story arc. But we'll see what happens.