We know from the story of Ariana's accidental burst of magic in front of the muggle boys, and what happened thereafter, that Albus's father was a man prone to violence. It wouldn't surprise me if the fistfight at Ariana's funeral were the second time his nose had been broken, not the first. It would explain a number of other things about Dumbledore, as well, for example:
-Why he sometimes acts in a more effeminate manner. His primary example of masculinity in his childhood was subconsciously linked towards violence and pain, whereas his mother would have been his symbol of safety and love.
-Why he is so insistent on Sirius staying in the house where the Black was (presumably) verbally if not physically abused by his own parents. He would consider Sirius's putting himself in potential danger to see some "action" (and thereby risking Harry's only connection to living "family") akin to his plans to abandon Ariana in search of personal glory. He empathizes with Sirius's hatred for his childhood home, but cannot let the same mistakes happen twice.
-Why he sometimes uses questionable moral judgment and falls to the dangerous "needs of the many" rationality; without a proper guiding male role model in his early childhood to teach him right from wrong, his concept of morality would have been developed largely by his own trial-and-error.
-Why he was so easily infatuated with Grindelwald. Until that point his idea of powerful masculinity would have probably been one of brute force; Grindelwald represented to him an image of male perfection– intelligent, strong, determined, and refined– as opposed to his father.
-Why he puts off telling Harry the ugly truths of who he is for as long as possible. He wants to shelter Harry as much as he possibly can, rather than exposing him to the ugliness of the world very young, the way that he was.
-Why he is willing to leave Harry with the Dursleys, despite knowing that they are rude to him and at times even neglectful. Compared to his childhood home, the Dursleys probably seemed like the lap of luxury.
-Even why he is so fond of sweets. Five galleons says that the Dumbledore children didn't often get candy at home, seeing as there wasn't money for it.
So it's my theory that at some point in his youth, Dumbledore's father hit him in a moment of anger and accidentally broke his nose. It was never fixed because neither of his parents knew how to do it properly (yes, Tonks can mend bones and Hermione glasses, but bones are probably harder and Tonks is an auror), and they didn't want to have to explain the situation to the healers at St. Mungo's. Then at Ariana's funeral, he and Aberforth got into a fistfight and it got broken again. *Shrugs**