If you were feeling charitable towards Harry, you'd say that he is concerned because William does not know what it's like to be 'not the heir'. And I think it probably is intrinsically hard to be 'nearly the special one'. Especially when they are just your annoying older brother or sister.
The dynamic is different in the generation above Harry possibly because Anne was a girl, in an era when lots of families gave preferential treatment to boys. In interviews with her, it's very clear she was brought up to know her place in the family, and doesn't see that as a bad thing. Andrew and Edward are 12 and 16 years younger than Charles. They are essentially two separate sets of childhoods. For Harry and William's generation, it's much more normal to treat your children as equals and Diana and Charles probably did try to do that. But it clashes with how things work in terms of inheriting the crown. William and Harry are not equals in the Royal Family.
As with others though, you can't comment negatively on how your sibling parents their children and expect it to go down well.
Although Harry is has insight into being brought up as the spare in the British Royal Family, his experience has many unique features that Charlotte and Louis (hopefully) won't experience, on top of which society is not quite the same now as it was then. There are plenty of other European royals navigating similar challenges in the 2020s who are likely to be sympathetic. William and Kate have met most of them. If they wanted advice, they could find it.