I am one of two directors and 50% shareholders in my corporation, but the two of us can’t agree on anything. What can we do?

Most states have statutory provisions specifically addressing the problem of “deadlocked” directors and/or shareholders. In California, for example, in the situation you described, which is not uncommon, you may petition the local court to appoint a provisional director. See Cal. Corp. Code § 308. The provisional director is an impartial person (not a creditor of the corporation or a relative of you or the other director/shareholder or the judge) who has all the rights and powers of another director and acts as such until the deadlock in the board and/or among the shareholders is broken or the provisional director is removed by the court or by the shareholders, if they can finally get together and break the stalemate. The provisional director is entitled to be compensated for her time, so this is not an ideal solution in any way, though it may be a necessary one and may spur you and your partner on to resolve your differences.