This is a matter of semantics, but if the "mathematically right" answer is also the wrong answer, than your math is wrong. Either you messed up the calculations

This is a matter of semantics, but if the "mathematically right" answer is also the wrong answer, than your math is wrong. Either you messed up the calculations, or (as is the case here) you started off with invalid assumptions. In this case, the invalid assumption is that you're psychologically able to do whatever will pay off your debts in the most money-maximizing way.