I am more of a dog person than a cat person. How about you?
Dog people and cat people is a concept of a person's animal or pet preference 
I know! Which one do you classify yourself as?
my personality trait is a dog person
Same here. I do love cats too though, but I know some people who strictly like dogs and not cats, and vice versa.
True. Some people base an important portion of their identity around the dog or cat  
I know I am one of those people. I actually volunteer at animal shelters as a dog walker in my spare time.
Really? This two terms refers to people of self identification