To be fair johnny didnt have to push him to the ground at the beginning. Though if daniel were smart he would realize if Johnny really wanted to hurt him he could but didnt. (Until daniel chose to escalate the fight)
I wonder what miyagi would have thought if he knew what daniel did back in the bathroom.
Daniel didn't want to look like a wimp in front of the girl. But it is true that he repeatedly escalated the situation on purpose because of his ego issues. Mr. Miyagi tried to help him overcome his insecurities and his need to resort to fighting in order to prove something, as a first step to becoming a souvereign Karate master one day. Of course, we could talk about how far he succeded in the course of the three movies...