Question

What were some advantages of domesticating animals instead of hunting them

Answer 1

It was a way to have a constant supply of items like eggs or milk.
Domestication also meant the possibility of breeding animals. They didn't have to hunt if they already had them in captivity. There was no refrigeration, so keeping the animals alive ensured they would remain fresh. Skin and wool made leather and other clothing items. Manure to improve crops became readily available. Every part of an animal slaughtered was out to use. As tallow, needles, sinew/ thread, tools, glue.
Dogs/wolves helped humans hunt rather than compete.

People no longer had to migrate with the animals. They could settle and farm.