This is a great photo of a subtle example of dislike of the question or questioner. Here, President Obama has his head slightly turned away from the reporter during a press conference in the East Room of the White House. We have a strong tendency to not look directly at those whom we don't like, don't trust, disrespect or when reliability or motive is questioned. President Obama shows us another subtle sign which is congruent with a head turn in this context - a very slight narrowing of the eye opening/coming together of the eyelids. If this were a video, we would see its very fleeting and dynamic nature. There is often a simultaneous pulling back of the head (very subtle here) and a slight tightening of the face in the "mustache area". As this emotion grows, this tightening will progress to include nostril dilation (not present here) which is indicative of disgust, or contempt if it's unilateral.
Like most modern presidents, Mr. Obama is very skilled at the nuances of expressing what he wants in any given situation - and yet even the Masters will display tells. Most everyone can see extreme examples of emotion, but it continues to amaze me how few otherwise social adept and skilled people can spot moderate, let alone subtle examples of very common emotions. This is one of the great advantages of becoming proficient at body language - for the emotions are still present - they're just being camouflaged. Recognizing them will give you an extreme advantage.