I really wish my partner didn't walk around the house with his headphones on all the time.
What's wrong with him wearing his headphones around the house. Is he doing it for a reason?
He just doesn't want to talk to me.
It would be annoying to have a partner who wore headphones around the house so much. It's rude of him to try avoid talking to you. It seems like maybe he's not a great partner for you.
Goddammit, like I have time for this. He just needs to not be a prick.
It's understandable that you're so upset about it. You need to push him into a conversation about it and let him know how you feel or the problem will never get solved. If he doesn't want to change then it might be time to move on.