You are ignoring the n-order impacts like resource allocation. You are clearly not generating empathy for the animals that your pet is consuming. It also seems any positive impact is negligible give the current status quo.

"As long as the animal is also happy and cared for, then utilizing a relationship with a pet to cultivate empathy is a healthy, normal, pro-social behavior which makes the world a better place." emphasis mine

This is a highly speculative opinion that provides no cost benefit analysis.