My husband and I consider ourselves Mom and Dad to the pups. The reason I think this feeling comes about, is because we are their guardians and caretakers too. With a friend normally, you aren't responsible for feeding them, taking them to the doctor when they aren't feeling well, comforting them during a storm, or whatever. You also wouldn't tell a friend over visiting to stop that chewing on the sofa , as well as expecting some amount of obedience from them.

Kay also makes a good point in that they fill many roles too, at different times.

But overall, I feel a parent to my pets, because I am responsible for their well being, just as a parent is to their child. My pets are fully dependent upon me for food, exercise, affection, etc. etc.