Your brain is still developing when you're a child, which is why those years are often referred to as your formative years.
Harry wrote a memoir about his life, so naturally he's reflecting on his experiences and how he perceived them at the time. If he felt he was treated differently as a child, that's part of his story to tell. Sharing those experiences isn't moaning or whining, it's recounting his life as he remembers it.
If I were to write a memoir, I'd probably have things to say about being a middle child. I might talk about feeling left out at times or how the youngest was often seen as the favourite. My older sister would likely say she had it hardest because she was expected to set an example for the rest of us. We're all entitled to reflect on those experiences without being dismissed as complainers.
As for the sausage incident, I don't believe it was actually in the book. If I remember correctly, it came from an interview with Paul Burrell, who recalled seeing a nanny give William more sausages because he would one day be King. Any child exposed to that kind of dynamic is likely to feel less important or valued.
Psychologists have long discussed how parents often treat siblings differently, sometimes without even realising it, and birth order can play a role in that. But in this case, we're not talking about subtle differences. Imagine explicitly telling a child that their sibling gets more because they're more important. How many people would consider that healthy or fair?
It's fairly clear that the environment those children grew up in reinforced the idea that one sibling was the priority. That's not a criticism of William; it's an observation about the institution and expectations surrounding them.
It's asking a lot of any child to happily accept being treated as less important. To expect them to respond with complete emotional maturity and never feel hurt is unrealistic. Children simply don't have that level of emotional development, and it's perfectly understandable that those experiences would stay with them into adulthood.