This is not true.
We literally discovered a 32,000 year old burial site where a hunter put a mammoth bone in their deceased dogs mouth when they buried him.
https://www.boehringer-ingelheim.com/animal-health/our-respo...
That's not utilitarian, to give funerary care.
Another grave site in Germany from 14,000 years ago had a dog buried with a man and a woman, treating it as a family member.
We literally have had fur babies since before we had civilization.
Once you get there, there's far more evidence: ancient Greeks burying pets and writing inscriptions about how they loved them, dogs and baboons were kept as pets in ancient Egypt, and given names, which was a big deal in Egyptian religion, and wasn't done for utility animals at all.