Grieving for a pet is totally a thing.
Comparing its importance to that of a child might be taking it a little far. Nothing would compare to losing a child.
I agree with you. I can imagine that people without children that have pets might feel like it's similar, but there's definitely quite a few several hundreds of thousand of years of evolution driving very distinct reactions.
Losing a child must, by force of nature, be much more difficult to handle than even a 20+ year relationship with one's dearest horse or Galapagos turtle or tiger cub or something.
We also don't allow cloning children, no matter how much you miss them. It's an ethical quagmire, and doesn't really address the problem (dealing with grief is hard, transplanting that grief onto a surrogate creates more problems)
Losing a child must, by force of nature, be much more difficult to handle than even a 20+ year relationship with one's dearest horse or Galapagos turtle or tiger cub or something.
It is interesting to think about, in any case.