I know that losing a pet hurts a lot more than losing a grandparent or aunt or uncle when they're not ever-present in your life. I have not lost parents yet, but at this remove in my life they are in many ways just people I used to know - my personality and values are quite different to them and I find it hard to empathize with their life choices. I think losing them would be similar to losing the little kitten I reared from a few weeks old. The actual relationship with my parents is mostly dead already, because it's been decades since we were close.
It's not about losing a human Vs losing an animal. It's about losing a relationship that is part of your daily life.