@xSauriaNx
The Problem is, even IF the Prince just wants to get out of his Sisters shadow, the way he's doing it makes him look MORE incompetent, not less.
Openly completely humiliating the Daughter of who's probably the 2nd Most powerfull Noble in the Country by breaking off his Engagement with her, (even IF its important for his long-term plans), just makes him look not only extremely short-sighted, it also makes it look like he cares more about himself than those around him. Both things people don't exactly look for in rulers, for good reasons.
Volunteering to fight the dragon and raising his Reputation that way is the first remotely smart thing he's done.