DON’T ASK ME ABOUT DON’T ASK DON’T TELL

I have a question to ask for anyone who knows how the Executive Branch really works.  Regarding Don’t Ask Don’t Tell, the President said in his SOTU address that he would be asking Congress to repeal it.  That’s fine, but doesn’t the President have the authority to end it himself?  Can’t he just issue an executive order to end it?  And if he can, why won’t he?