On 7 December 2016, various web sites stories with headlines that suggested President Barack Obama had urged United States soldiers to question the authority of incoming president Donald Trump.
While Obama did tell troops gathered at MacDill Air Force Base in Florida on 6 December 2016 that they have the right to criticize the president and protest authority, he did not name Trump. As Obama is president until Trump is sworn in on 20 January 2017, he presumably could have been referring to himself. But because he said people have the right to criticize "a president" without reprisal, it's likely he was referring to the office of the president in general terms. He said:
We’re a nation that believes freedom can never be taken for granted and that each of us has a responsibility to sustain it. The universal right to speak your mind and to protest against authority, to live in a society that’s open and free, that can criticize a President without retribution -- (applause) -- a country where you're judged by the content of your character rather than what you look like, or how you worship, or what your last name is, or where your family came from -- that's what separates us from tyrants and terrorists.
Obama's words were relatively vague and described American notions of freedom of speech. While they did not seem to be aimed at any particular person other than "a president," they could be interpreted any number of ways, including to mean he was referring to Trump — although he never named Trump in the speech. It seems more likely the comments were blown out of proportion for maximum outrage value.
The transcript of Obama's speech can be read here, or it can be watched in its entirety here: