JF- you can and walk and play without the dog, and the dog adds a lot more stress and effort which decreases productivity. After all, you don’t need to stop every 10 minutes to clean up drek if you just take walks by yourself. Why do you assume one can only get exercise with a dog?
Cleaning up after a dog (along with everything else I mentioned) is a waste of time and it dirties up your house, and as I said is bittul Torah. It’s not my achrayus if I don’t own a dog, it only becomes my achrayus if I, engaging in bittul torah and zman, buy a dog!
Regarding your name, feminist theory advocates for full equality and rights for women. Associating Judaism with that ideology doesn’t make sense, as halacha has a lot to say about gender roles, and it ain’t feminism.