Brabantio doesn't want Desdemona to marry Othello because he is racist. In this Shakespearean world, Othello could be applauded for his great triumphs at war but he certainly couldn't marry a white man's daughter. Remember that Othello was a Moor. Typically, Moors were a people from Northern Africa. Othello would have been dark skinned and from a far different culture. It is likely that he was even of a different religion because many of the Moors were Muslim while most of Europe was Catholic. We see evidence of Brabantio's racism when he tells Roderigo, a man he has forbidden to pursue his daughter, that he wishes he had allowed the match rather than watch Desdemona marry Othello. In fact, Brabantio is so shocked by his daughter's choice that he accuses Othello of bewitching her. Surely his precious daughter would not choose to marry someone like Othello. Of course, Desdemona does not share her father's prejudice and seems to truly care for her new husband.