The reason not to do this is that you're very likely to provoke a defensive response and have the other person dig in their heels. A gentler approach is more likely to get results, less likely to create tension in the relationship, and sets the tone of future decision making as adversarial.
If that doesn't work you can try firmer approaches, and you can of course always quit or use the threat of quitting, but 99 times out of 100 leading with that will lead to worse outcomes.
You don't give up any leverage by first trying to resolve conflicts without threats.