Why is a push in the back that sends a player jumping up for the ball away from it, a soft penalty. A soft penalty is when there is slight contact and someone goes down. The push wasn't slight.
Look up the definition of 'Laws'.
As for the referee, he was typical of most refs, very weak. Players will always try and push the boundaries and it's up to the ref to make sure they don't. Do it early on and set the standard, let it go and no one knows what they can and cannot do.