I *think* I understand where the OP is coming from, and to an extent I do agree that the comparison can be irksome.
I'll never forget a member on here lost a child shortly after birth and received the comment from someone IRL "I know how you feel, my dog died last week". In this context, I think it's absolutely not okay to consider a human baby and a pet comparable.
I recently posted a thread because I found it a bit irritating that my mother refers to her Labradors as "the kids", as my mother obviously has her own children! I received mixed responses, but a number of posters did agree that it didn't sit well with them.
There are people who have 'fur babies' because they can't have children of their own. I'm very sympathetic to this. No way should anyone try and challenge their love for their pets.
In my opinion, the responsibility of raising a human child is not really comparable to having a pet. I do not however question the genuine love that people have for their pets can be as strong as the love a person experiences for their own human offspring. But it is a different love. We know when we invite a pet into our hearts that we will outlive them, and when they pass on we can welcome another pet into our home to replace them. A child is expected to be part of you for the rest of your natural life and is in no way, shape or form replaceable.
To summarise, in some contexts I do find it annoying because I feel a human life holds greater value and responsibility than the life of a pet.