What do you say in a job interview when asked why did you resign from your old company?

Be honest and tell them the details. Being honest is important, but it's also important to do it without seeming as if you are bashing your former employer. In other Words, if your former employer was a total jerk, just say that you and he had your differences. Then, if the one interviewing you wants to know what sort of differences, tell the truth, but with as much tact and respect towards your former employer as possible. Otherwise, you may come off sounding like a dissatisfied trouble maker, even if you aren't.