If everything dies, at some level killing isn't such a sin. There are real practical populations if people use that as a serious philosophical starting point though.
Beyond that, your rat depends on you as a pet. I’m afraid that, if you can’t adequately look after your pets because of your beliefs, then you shouldn’t have pets.
There's the obvious self-defense exceptions, if a lion or a person would attack me or my family I would shoot him, but an enlightened being may act differently because they may understand something we don't.
I definitely recommend https://www.amazon.com/Guide-Good-Life-Ancient-Stoic-ebook/d....
I agree and should have agreed differently that an absence of attachment does not mean an absence of love.