The phrase "for me to be an animal" may sound nonsensical, but "why am I me, rather than an animal?" is not obviously sillier than "why am I me, rather than a person from the far future?".

Agreed - they are both equally silly. The only answer I can think of is 'How do you know you are not?" If you had, in fact, been turned into an animal, and an animal into you, what differences would you expect to see in the world?