Before I had children, I felt that way toward my cat. When I had kids, I actually developed an antagonistic attitude towards the pets I had at the time. Since then, it is very difficult for me to compare pets with children. Theoretically I can get it, and I am very good at giving sympathy but I just can't feel it, and basically it boils down to this: As a pet owner, if life progresses normally, you will almost certainly outlive your pet. You know logically at the time you become the pet owner that one day you will sadly have to say goodbye. As a parent, you are not supposed to outlive your children. In that regard, our relationship with our fur babies can never really be like the relationship we have with human children.
Not having children in no way diminishes the value or nurturing capabilities that someone has! It just isn't fair to compare parenting with pet ownership, no matter how easy it is to try that comparison. I also think it is a big emotional risk and potentially unhealthy to put too much of the parent/child expectations into a pet relationship, especially given the fact you will almost certainly outlive your pet. It is just asking for heartache