Bane is a wild-looking centaur who really, truly, profoundly hates humans. He hates humans so much that he wants to kill Harry, Hermione, and Hagrid the night they all go to visit Grawp for the first time in the Forbidden Forest. Even though Magorian protests that Harry and Hermione are just children, Bane still feels that "they have probably already profited from the traitor Firenze's teachings" (30.217) and that they deserve to die. Bane is not one for compromise.
Bane's strong anti-human sentiment leads to bad news for Professor Umbridge, who is "borne away through the trees by Bane" (33.46) when Hermione lures her into the forest with the promise of a new weapon. Bane's strongly anti-human sentiment is only matched by Professor Umbridge's own arrogance and prejudice against half-humans. So, it makes sense that a meeting between these two extremists can only end in violence.