Harr’s accusation of William pushing him sounds very similar to what Harry did to a photographer, which was caught on camera. Apparently, Harry was already in the car when he decided to step out and push the photographer unprovoked. That photographer ended up with a bruise or cut, and I think he went to the police about it.
Also, Harry has claimed that he slapped his bodyguard when he was drunk, and has also been accused of slapping one of the foo fighters. Also all unprovoked.
It's clear that Harry has a violent temper, and physically attacks people whenever he feels like it.
Meanwhile, the only time we got to see William lose his temper in public was when the paparazzi was stalking him and his family, and even then he was very restrained.
As for the claim that the press never reports on william’s escapades, that's clearly not the case because he's been caught many times when he was younger, looking drunk and stumbling into cars with a drunk looking kate. He's been caught dancing awkwardly in bars, and his and kate’s phones were hacked more times than harry’s was.
Not to mention that paparazzi took photos of him on his honeymoon with kate. So no, the press haven't always been kind to William or to kate. Theyre just not foolish enough to do things like hurl racial slurs, or wear Nazi costumes, or compare the taliban to chess pieces, nor are they shameless enough to come up with over the top statements that evokes images of Diana’s car crash.