I bet part of that was an emotion completely absent from Trump's public persona: shame.
Trump started his political career circa 2010 as a "birther" -- going on national TV, asking for Obama's birth certificate, saying he was born in Kenya and therefore ineligible to hold office. Really racist, bottom-of-the-barrel tabloid stuff.
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Obama was incredibly gracious the day after the election. Here he is, talking about how he's "rooting" for Trump to do well, how Trump's success as President will be the nation's success:
https://www.youtube.com/watch?v=Wr2USTE3L98
Meeting after all that must have been at least a little bit embarrassing. Even for the Donald.