No, Momof2inPA, I do not consider my dog and cats to be the "equivalent" of human children. As the doting aunt of 7, I understand the difference between animals and people. But just maybe, having pets is a good exposure to some of the responsibilities that go along with the joys of parenting.
When I decided to adopt my pets, I had to think about all of the things it meant: I'd have to pay to feed them, provide appropriate shelter and medical care for them (including making sure they do not suffer when they come to the end of their days; make sure were looked after when I was working and when I was on vacation in places where pets aren't welcomed. I would be responsible for training them to behave, so that they wouldn't create problems for me or for the people with whom they might come into contact. I had to ensure that I would have time to spend with them every day, so that they would be sociable with people. I had to realize that there were a lot of places that I couldn't (or shouldn't) bring them. I had to realize that when I did find places (e.g., hotels) that WERE friendly to pets, it was my responsibility to ensure that they behaved well so as not to spoil the experience for non-pet owners and for future visitors who would want to bring their pets. I knew that I was the one who would be responsible for cleaning up after them. I knew it was also my responsibility to prevent my pets from roaming around unsupervised, creating hazards and messes in other people's space, on the roads, etc. Having thought about all of these things, I decided I was willing to accept them, and my dog and two cats are an important part of my family. They are not my friends, they are not human children, but they are creatures who I love and am responsible for -- both for their sakes, and for the sake of society at large.
If all pet owners thought about these things before they adopted pets, there would be a lot fewer animals causing problems. Come to think of it, maybe people should think about a lot of the same issues before they have children ...