I don't feel that animal are more important than humans. I do think that how seriously we take our responsibilities with regards to our animals can say a lot about us as people. I am not someone who regards my pets as "members of the family" or "children". I do, however, appreciate the unconditional love of my pets for what it is.
Growing up we generally had a dog - 1st was a beagle/dachsund mutt (adopted from a family that was moving), put down at the age of 6 when her 3rd slipped disc refused to respond to treatment (took me a long time to forgive mom for not telling me the day she was going to be put down [I was in 5th grade]...she thought it would be easier for me to not know). 2nd was a husky/beagle (?) mutt from the pound (that was a very interesting looking dog! - looked like a dingo with one blue eye, one brown, ears stood straight up and were huge - like bat ears).
MrS and I adopted a German Shepherd/Rotty mutt from the humane society when we moved to our first apt. When we were going to be gone longer during the day (I was starting my clinical rotations) we got her a pet kitten (also from the humane society) to keep her company (our lease actually specified "only one dog" - didn't say anything about cats) - OMG they were so attached to each other! Dog had to be put down at 11 yrs old due to pericardial effusion from a heart tumor. Cat dropped dead (literally - it was bizarre, fell off the couch... dead) a few weeks later.
Currently we have a boxer/pit bull type mutt (from the humane society) and her cat (also from the humane society) as well as her puppy - a collie/English shepherd mutt that randomly showed up at our back door (we live in the country). (Dog#1 doesn't generally get along with other dogs - so the fact that she accepted this puppy seemed like a sign. We did track down his former owner - 5 miles away - and leaving him with us was the best option available.) We also have a snake (have had other snakes/reptiles/amphibians/fish/rodents/ferrets along the way - but they don't give you nearly the lovin' that dogs and cats do - although my rat lived over 5 years and was, in his way, very affectionate).
We may not be the bestest pet parents in the world (training leaves a lot to be desired
) - but our animals visit the vet regularly, are fixed, shots are up to date, get their heartworm pills, and none of them are overweight. Dogs have giant overhead runs outside and their own room in the house for when we are not there (plan is for a dog door to a large outside kennel in the future - for long days at work or overnights). Cat is indoors only and not declawed.
Are they "more important" to me than people? No. Do I take my responsibilities to them seriously? Yes.