"Family quarrels are bitter things. They don't go according to any rules" (F. Scott Fitzgerald)
A company's directors have both the power and the duty to manage the company's affairs for its benefit.
When two or more directors are in place, it's perhaps natural for the occasional disagreement to arise between them. Indeed, regular expression of a variety of different viewpoints and ideas can make for a strong, dynamic board and business. Provided, that is, that the directors are in the end result still able to agree on the decisions vital to their company's continued operations.