There is to be cooperation, sympathy, and appreciation of the other. If you don't think that, then you will not have a lasting marriage. Rather, a quick divorce. So be patient. Patience is what you have when the board member you dislike is wrong.
Marriage is really a pretty good analogy.
Just as quarrels are inevitable in marriages, so there will be quarrels in your relationship with the board. The key to survival is to make sure that your words are kind and gentle today because you may have to eat them tomorrow. Difficulties rarely arise from a single cause. A breakup comes only over time. Hey, relax, if you're ever out of work.