Actually thinking about it I think he’s always felt inferior to William.
William was more able, better looking, found a wonderful gf who stuck by him. He was his mothers confidante. William was able to have his career of choice for years and live away from the limelight. He got a better choice of houses. William was never in trouble when young as Harry was.
I think he saw Meghan as an amazing prize and he couldn’t believe his luck. Then she started to feed his paranoia and sense of inferiority and he became angry and aggrieved. When his prize wasn’t thought to be as great as first believed by the family and public, he took it personally.
He’s out for recompense for everything he feels he didn’t get.