This is sort of why me and my wife pick fights with our kids where we can. We stress them to the point of snapping, then cool them down. It feels a little like bullying, but we cut back and emphasize that we still love them.

My 5 year old daughter in particular inherits the stubbornness of both her parents. She often she says something she regrets immediately (e.g "I hate you!"), cries on realizing it, but refuses to take it back.

We teach them that disagreements are perfectly normal. Differences in opinion should be embraced. And while you disagree with someone, you don't take it personally and dislike the person.

Shows like My Little Pony are excellent at this. While these shows have a villain and plot, the drama and conflict in most of the episodes revolve around growing up and dealing with stark personality differences. Friends will argue a lot, but the shows highlight that this doesn't end a friendship. And even someone who was 'evil' can turn over a new leaf.

She had a rough first week of school. Was picked on by a classmate, admitted she spent much of the day crying. But she goes home, opens up My Little Pony for inspiration. Then she's excited to go to school again. A couple of weeks later, she has solved the conflict with her classmate.