Is there a relationship between a pet owner's personality and the species of the pet?

The way I see it, it's mostly about upbringing and forced gender stereotypes. Men will like "tough", "cool" animals, while women go for "cute". Which I think it's really sad, since it would be best if everyone chose pets based on their personalities. Dogs are the most popular pet mostly because of tradition, I notice that a lot of dog owners don't have the patience for the dogs liveliness. Having a dog is almost like having a child, but a lot of people don't seem to realize that. Choosing a pet based on your personality would be ideal, since only then would the pet be a true companion, and both the guardian and the pet would be a lot happier.
I choose cats since they're more independent, and I can leave them for half a day if I need to without worry that they're lonely. They were on the perfect level of independence and cuddliness for me. The next pet I get might be even lower maintenance, like a tortoise, since I might be a bit too lazy even for cats.