The minotaur adventures because he was outcast from his home. He grew up in a small village of minotaurs. While he was young, life was peaceful and good. He never seemed to fit in, though. He never felt totally comfortable around others and was even distant from his family members. He had very few friends. No one really worried about it, though, because he seemed normal and didn't cause trouble.
Things changed when he was 12. A small war party of giants came to the village to reclaim their rightful servants. The village was able to fend the giants off, but several members of the minotaur's family were killed, including his father and his younger brother who was closer to him than anyone else. Something inside the young minotaur seemed to snap. He became consumed with a fiery rage. He preached loudly and frequently for war with the giants. He got into fights frequently and became a drunkard as he grew older.
The village elders tried to help the minotaur channel his rage by training him in the warrior arts, hunting, and tracking. It only seemed to fuel his anger, though. One day, he ambushed and slew several young hill giants. The minotaur village was attacked in retribution and many minotaurs were slain. The village elders summoned the minotaur and told him that he was outcast from the village. He could not return until he learned to deal with the hate, anger, and rage festering inside of him. Cursing the elders he left.
Now, he wanders the country, alternately drowning his anger in drink or getting into fights. Deep down he knows he is on a self-destructive path, but he doesn't know how to change.