I was thinking something similar to the pet analogy as well, but where I'm something a little less interactive than a dog, like something you keep in a cage.

I think he meant "the way you feel love towards me is different than how I feel love towards you" because he was talking before that about the inherent imbalance in the therapist-client relationship.

I agree maybe defining "love" might be a place to start. I think I'd need to come up with my own definition first.