A stray cat wants to be inside my house

There’s a stray cat that I’ve been feeding for a while now. He’s pretty young and it’s kind of weird watching him grow. Problem is, my dad doesn’t want pets especially any strays. My mom likes the cat and feeds him too and pets him but we aren’t allowed to bring him inside the house. Me and my mom tried once and just kept him in a storage room so he can stay out of the cold (it was when there was Icey snow everywhere), but my dad found him and was pretty mad about it.

I already got him a house to stay in but he doesn’t want to be in it. He just sits at my door and waits for me to come outside. I pet him and hold him whenever I see him and also got him toys to play with but he doesn’t want any of that and just wants to walk around my house.

I’m not sure what I should do here. He wasn’t this persistent on trying to get inside my house before. He’s just sitting outside my front door waiting instead of going inside the house. I figured it might be wet so I got some towels to put on the inside but he still doesn’t want to be in there.