The tyrannical Captain Jaggery hates Zachariah for a number of reasons. For one thing, he can't dominate him the way he can with other members of the ship's crew, and for a control freak like Jaggery, that's a serious problem.
There's no doubt that race also plays a part in Jaggery's animosity towards Zachariah. As the only black man on board the ship, Zachariah is particularly vulnerable to discrimination. A notably outrageous example of this occurs when Zachariah is made a scapegoat for a mutiny and is brutally punished by Jaggery and the sadistic Mr. Hollybrass, who string him up and whip him without mercy. Zachariah's not a slave, but Jaggery certainly treats him like one. The truth is that the Captain doesn't see him as an equal and so doesn't feel the need to treat him accordingly.