“Humans didn’t kill off the cats ~ hunger killed them!”
The two aren’t mutually exclusive, since we are predators competing for the same food sources, and humans have proved to be more effective in most circumstances. The cats have had to retreat to places with enough food to support us both, or where they have a clear advantage over us.
Also, your theory doesn’t explain why big cats died out in the Mid-east and Mediterranean long after the glacial periods were over, but at the same time that human societies were becoming more advanced technologically.
Try CAT DISTEMPER
Lo and behold there were still some of these dudes around in Medieval times BUT THEY WERE TOO LARGE TO PROCESS ~ so we selected for smaller cows and bulls.
Recently someone began a project to breed back to the giant Aurochs.
Humans have an edge on the other predators no one in all of history or prehistory had ~ we can actually modify the prey animals to fit our capabilities.
The big cats were DOOMED ~ eventually.
In this case I think the Younger Dryas killed them off by killing their prey. They had nothing left to eat that was easy for them to catch.