No one owes Trump an apology. Trump owes the citizens of the United States an apology for stirring up discord, and bringing overt corruption into the office of the president.

I agree with you that in this case, Trump wasn't being sexist so much as egotistical. Trump even told an interviewer that he "wanted to put his own mark on the Fed. He chose a chairman who approved of the very cautious and prudent policies of Janet Yellen, not, in my opinion, so much based on gender. However, President Obama put far more women in powerful positions than Trump has, so far.