Oh screw the idea that she's just younger than him, she's in high school. She's not a 22 year old he met at the office, she's literally in high school. She just turned 18 and was living with him before that. You want to blow up both his life and hers? Start making noise about that. What she's talking about is going to meet her parents and explain to them that they're not engaged anymore, and she opened the whole conversation there with a pretty serious implied threat about how young Nina is and the issues that it could cause.I think a lot of the comments here are kind of missing this context/perspective. Aoba is a victim of more than just cheating, his last relationship was beyond unhealthy to the point it traumatized him, it's kind of clear why he isn't able to think about it clearly. Beyond that, it's not like his relationship with Nina is super straightforward either given that she's younger and also happens to be the person behind a Vtuber he liked. It's hard for me to think anything other than that he's got it rough.
One of the things about the manga is how much Ao understands, appreciates, and works around this. Nina is often the driving force in the relationship because Ao is deeply aware of how the situation would be perceived and the problems it would cause for her. Blowing off your ex-fiancée's request to talk to her parents about why you're not engaged anymore to go see fireworks with a highschooler you live with is, straight up, not a good look for an adult.