I have always felt sorry for people who do not have a bond with animals. I feel there is a facet of life they are missing out on.
Oddly enough, when I have lost a pet, and I lost 2 cats in the last 3 years, I weep and wail most uncontrollably. I think I've been giving myself permission to mourn for more than just the loss of a beloved pet. Certainly in the loss of my avatar, Loki, I was incredibly distraught. I think I was also mourning the loss of my mother, who was still alive at that point.