𝐊𝐀𝐓𝐒𝐔𝐊𝐈 is not the most touchy person in general so it might take a while for you to realize that he tends to stay away from specific kinds of physical contact
he's not opposed to cuddling, he even initiates it from time to time, opening up his arms while you're near -face carefully neutral, almost annoyed- silently signaling for you to step into his arms so that he can hold you
will tell you to fuck off while actively pulling you closer against his chest, careful as to not accidentally squish you with his strong arms, never holding on long enough for any stupid extras to comment on it though
when the two of you are walking together 𝐊𝐀𝐓𝐒𝐔𝐊𝐈 will often put his arm around your shoulder
it’s very obvious that he also let's you get away with way more than anybody else
𝐊𝐀𝐓𝐒𝐔𝐊𝐈 might pretend to hate your attention but he secretly enjoys it
not only letting you play with his hair but also subconsciously leaning closer -albeit with a scowl on his face- while you run your fingers through his spikes or playing with the hem of his shirt when you're next to him, giving your hands something to do to keep you busy
but if there is one thing 𝐊𝐀𝐓𝐒𝐔𝐊𝐈 absolutely hates it’s holding hands
he’s not against the idea of hand holding in theory since it’s a very subtle way of showing affection
but due to training and his quirk his hands are really rough and always sweaty and he just thinks that holding his hand wouldn’t be a very enjoyable experience
no matter how hard he tries to convince himself that he doesn’t care about what others think of him at the end of the day 𝐊𝐀𝐓𝐒𝐔𝐊𝐈 just doesn’t want you to think he’s gross
and that reasoning doesn’t even include the potential danger of his quirk, he’s scared that he could lose control or that he can’t hold back and accidentally set of one of his explosions and hurt you
𝐊𝐀𝐓𝐒𝐔𝐊𝐈 and you both know that he’d never purposefully hurt you but he also just wants you to be safe, even if he has to keep you safe from his quirk, so you follow his lead and just hold onto his arm instead or seek contact in other ways
it’s not like his reluctance to hold your hand will ruin your relationship, after all there’s many ways to be affectionate and 𝐊𝐀𝐓𝐒𝐔𝐊𝐈 is determined to show you just how much you mean to him