Seems to me that this shouldve been a perfect case of having 3 crew members to resolve an issue between 2 of them. If the S/O had either incorrectly entered the wrong data, or The captain believed that they had...... Well then as the Capt and S/O stand their ground, the F/O steps in and makes an independent assessment..... Effectively becoming the umpire.
Of course these issues are never as straight forward as this, and quite possibly there is some background of past history involved.
Remember the last resort (and yes it can be viewed as extreme..... Especially for a S/O) is to pick up your nav bag and walk off the flight deck. After that it doesn't matter what happens. Call your ops dept, HR etc and explain the situation. No airline wants an aircraft to depart with the crew at each others throats!