It sounds like all good fun...but it really isn't. Years back I lost my Champion Collie to a squirrel. It used to taunt Joey and he would chase it. He never it catch it, but one day during the chase the squirrel jumped from the fence, over Joey's head, and into the tree behind him. Joey, of course, jumped trying to catch it. He snapped his head back trying to get it in that instant when it was airborne....and broke his own neck. Sadly, even a neurosurgeon was not able to save him, and he crossed over the Rainbow Bridge a few days later.
So while chasing squirrels seems like an innocent game, it can have heartbreaking consequences.
Rusty