I still don't understand what it means to claim that a president is "illegitimate."
Considering that the current President was politically rewarded in spite of his nakedly crass and racist trolling about the previous (black, Democratic) President's birth certificate and college transcripts (or let's be real,
because of said trolling - at least, initially in the development of his recent mass media-based self-promoting political hucksterism, which quickly turned into a successful career as a politician (though what's the difference these days?)), I think it's understandable - though rather petty and ultimately counterproductive - for a lot of Democrats/Obama supporters to feel this way toward Trump.
(This isn't taking into account the griping about the Electoral College as well as the Vast
Right-Wing FBI/Russia/WikiLeaks Conspiracy that supposedly installed Donald Trump as President.)