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.

It is interesting to think about, in any case.