It is one thing to appreciate a person's qualities from afar (or maybe not so afar, since Brabantio had received Othello as an honored guest in his home), but quite another matter to accept that person as a member of one's family. By displaying this contradictory trait in Brabantio, Shakespeare is skillfully holding the mirror up to all of us, not just citizens of 16th century England. We, in our modern society, still struggle with this sort of "two-faced" prejudice today.
That said, Brabantio not only decries the marriage (since it was completely improper for a daughter to elope without securing her father's blessing and permission), but goes further and accuses Othello of bewitching his daughter in order to get her to marry him:
She is abus'd, stol'n from me and corrupted
By spells and medicines, bought of mountebanks,
For nature so preposterously to err...
Sans witchcraft could not.
...I therefore vouch again,
That some mixture powerful o'er the blood,
Or with some dram conjur'd to this effect,
He wrought upon her.
Certainly, Brabantio is making reference to the impossibility of his daughter falling in love with a black man. But it is the witchcraft that he is objecting to before the Duke.
It is up to Othello and Desdemona to convince the Duke that they are married for love, not by the benefits of witchcraft and potions. And Othello's speech to the Duke, explaining the real situation of love between himself and Desdemona, is one of the most powerful and beautiful in all of Shakespeare (Act I, Scene iii, lines 128 - 170).