I get annoyed when someone says that's like bathing in your own filth

Bum juice? It's not like you're bathing in your own enema or something. Yes, there will be bits of dirt from all over your body in the tub, but it's extremely dilute.

Since there are no known diseases that come from water which has touched the outside of your asshole touching another part of your skin, nor is there any other detectable sign that this has happened, I assume he has a problem with the idea, not any real concerns about the effects. If you think about that even medium hard, though, it's ridiculous to think of baths as being particularly gross. He touches air that's touched his asshole all the time. He breathes air that has particles from other people's assholes in it. Every time he smells a fart, there are gasses and particles directly from somebody's asshole going inside his lungs. Everything he touches has touched something that has touched somebody's asshole. Every time he eats, he's consuming molecules that have been eaten and shat out repeatedly by countless animals' assholes.

Nothing on this planet is new: it's all been touched by billions of assholes. All water on Earth is asshole water. If he's such a special princess who has to shower in asshole free water, he can go melt some from the ice caps on Mars. Careful though, if Mars turns out to have had life in the past, that water might have touched alien assholes.

You dad is just being a little bitch he doesn't want to pay the utility bill to fill the whole tub up with hot water.