Rebel is a strong word. Some people just have different opinions or a different view of life than their parents. Sometimes the children grew up in a very different experience or world. I see this a lot with poor immigrant families who come to the US, the children are Americanised and assimilated more than the parents, they might have a higher education compared to the parents, and more interaction with varied opinions. Sometimes it is referred to as the parents having “old world” views. So the children don’t necessarily rebel, but they have a very different perspective on life, ettiquette, sometimes politics amd religion.
Children who rebel, or spite their parents, I think many times feel very restricted and confined by their parents. Extreme rebellion is their way to break free, find their independence and autonomy. It is like an extreme adolescense I think.
Of course if the parents are truly bad people with low integrity, then it is logical for the child to completely break free and live a different life. But, that is an extreme circumstance, which I assume you are not discussing within the realm of this question.