Ithink people are getting a bit mixed up.
Sure, some little;e kids have always played at being animals, they come up with it themselves. Or characters from cartoons like Lion King.
The therian thing though seems to come right from the adult scene which is very much about some of the alternate identities, and is also very often tied up in alternate sexual identities. It is desperate to legitimize itself by drawing in young people.
There is also some relation to certain kinds of anime which seems to be filled with creepy men - this is largely I expect related to some of the really nasty school girl sexual fetishes found within some anime.
And honestly, the who comic con culture and cosplay culture seems to be rife with a lot of it. Not that everyone is into it, but I think there is some very unhealthy alternate identity activity going on with a lot of people at these events now.
I was big into RPGs when I was young and loved the old school comic cons, but I find they've become a little worrying, There were always plenty of nerdy guys (mostly nerdy guys) but now so many seems to be drawn into some very odd directions. I suppose it's the internet.