[BradyLS]

I'm guessing Trump offered MLK III his to shake. Why otherwise would he have it out? Shaking hands his a stronger gesture between two people than just "thumbs up." For whatever reason, the offer wasn't picked up. Rather than look awkward with his hand out, Trump gives a "thumbs up."

[Robert DeLong]

Trump does a lot of thumbs up, sort of like his signature pose. That may be because I've have heard that he really does not like to shake hands with anyone. Supposedly like Howard Hughes, and the fictional detective Monk, he is a germaphobe.

20 Badass Handshakes by Donald J. Trump

Donald J. Trump is a nationally renowned businessman who has been successful despite his aversion to one common business practice...
The handshake.

2. Germs are worse than exercise

Donald Trump, who has on many occasions called the tradition of shaking hands “barbaric,” confessed in his 1997 book The Art of the Comeback: “One of the curses of American society is the simple act of shaking hands, and the more successful and famous one becomes the worse this terrible custom seems to get. I happen to be a clean hands freak. I feel much better after I thoroughly wash my hands, which I do as much as possible.”

But Trump’s germophobia goes beyond an unwillingness to shake hands—an aversion he has had to forgo during his run for the presidency.

Trump Is Right About One Thing: Shaking Hands Is Kinda Gross

Donald Trump is a serial liar, rampant xenophobe, racist, misogynist, birther and... germaphobe?

The Republican front-runner has called himself a “clean hands freak” and has referred to hand-shaking as “one of the curses of American society.