Well, I'm not as familiar with Presbyterianism, specifically, but the notion that animals can't display "love, compassion, cooperation, and empathy" is not typical orthodox Christian teaching and obviously wrong. (I mean, did no one in your church growing up have a dog?)
But at the same time, I think it seems quite clear that humans are unique among animals. Just the fact that you and I are communicating about this should demonstrate that quite convincingly. But even that is just my personal opinion and is not creedal orthodox Christianity. A person can believe that animals and humans are the same (in whatever sense you mean here) and can still hit all the requirements of the creeds.