A good while ago I watched documentaries about humans and how they developed into what they are today.
The advantage humans had was their brain, they could make tools for different things, they had a social structure that worked and kept the group safe. They had to learn to think like the animals they hunted, to read them.
Nature still obviously had the hand in it back then. Some belief the reason we have people being "night owls" today comes from the time humans still lived in nature. They needed people to be awake at night and watch over. So some naturally developed that trait.
I can imagine some were better with reading animals than others. Even back then. Some were probably amazing with that.
So: I believe that's the origin of therianthropy today. Therians are the people that have the ability to see the world from an animals point of view, to the point of relating to them. Who wouldn't if you understand animal behavior very well and find a species that you can relate to on a personal level?