Aside from all the petty spite the thing that I think is one of the most offensive and hurtful for William is that Harry seems to want to claim Diana as only his mother. He wants everyone to believe William and Charles are two of a kind and so are he and Diana. In his book he talks about William's resemblance to Diana fading. Surely any child could accept that a parents "belongs" equally to all children? It's such a cruel narrative for him to push.
He must be so put out that William and Diana are so alike and he is looking more and more like Charles as he gets older!