I believe that if something is good in some way that I could enjoy it too, if I really want to. I may think videogames are a waste of time, but when I find myself a friends birthday party and they're busting out the games it's more important for me to have fun than make my silly point, and I'll be damned if I didn't have a great time!
Likewise, I feel that if people could get over the fact that classical music is old they would probably be able to enjoy it quite a bit, because it's just good stuff. The same goes for any style, if we can just get into the particular aesthetic perspective we can enjoy it too. I don't expect anyone to run off and buy a piano or start a Beethoven CD collection, but in the moment if they can get over their obstacles, they could enjoy it to some degree. If they want.
Practical advice: since people are generally predisposed to like what's familiar, if you start with something like fur elise or some other ridiculously famous piece, people will like it.
Also to play good. It doesn't matter how well a piece is written if it's being played badly, and consider that it might be trying for your dad to have to hear you practice day after day. I'm not trying to put you down or anything, but I know that I would have troubles having to listen to somebody else practice all the time.