I agree that it is creepy and subservient… but it is also entirely accurate. The dog is a pet. It is entirely reliant on the owner, and it is only allowed to do what the owner lets it do. It eats when the owner tells it to. It goes outside only when the owner says so. It probably even had its genitals removed at the request of the owner.

So yeah, ‘master’ is an appropriate word here.

I find it a bit uncomfortable too, which is why I don’t have a pet. But from what I can tell, dogs are generally fine with this arrangement. Most dogs seem to like it this way.