I honestly think that people who have never been in a situation like this guy has (having to move multiple times as a kid) won't really understand how he feels.
Like as someone who has had the same kind of childhood, I get it. Every move, I made friends, then I lost them later. We always promised to keep in touch but it never lasted long. Eventually I just started to be apathetic and refused to make long lasting relationships of any kind because I was afraid of constantly getting hurt again.
The MC here has lived like this for years. But suddenly, he finds a girl that likes him, and it takes him a while to open up to her. To actually like her back. And just when things are looking up, he has to move again. He's going to lose another relationship yet again. Normally, he would just be like "oh well, that sucks, same old." But now he actually doesn't want to just brush it off like before. He really wants to keep this relationship. But he's powerless, in the sense that he can't prevent his family moving. So he's desperate to try and do something, anything to keep a thread of that relationship. And right now, that line of thought has him think to go to the catgirl's dad, presumably for some sort of closure or way to keep them connected.
Does it make sense? From an outside perspective, not really. But as someone who has been in his shoes before, I understand his actions.
(Of course I could just have egg on my face if his talk with her dad is about something completely different than what I'm thinking but hey, that's life baybee)