Harry has a deep seated inferiority complex. And it’s not all down to being “the spare”. A lot of it is down to who he is and the choices he has made.
as children, William was much better looking and did much better at school. Harry had to repeat a year of school, which must have been embarrassing.
as young men, William went to university - Harry didn’t have the grades or the intelligence.
William did military service, then worked as an air ambulance pilot. Harry did service, then left because he could progress no further, due to his lack of intelligence.
William had a long term relationship with a girl from a stable and loving family, before he married her.
Harry had several failed relationships then married a woman who is estranged from most of her family.
telling all these petty and spiteful tales is giving him a sense of power, and he is relishing every moment of it.