This photo was taken in 2009 at the G20 Summit in Pittsburgh, Pennsylvania. A bit of background here: Silvio Berlusconi (on Left) is the Italian Prime Minister who has a reputation as a womanizer. Just prior to this moment at the G20 ceremonies, Mrs. Obama hugged and kissed the Brown's (then Prime Minister of The U.K. and his wife), the Medvedev's (Russian President and his Missus) the Sarkozy's (France's first couple) and Angela Merkel (Germany's Chancellor). Not only does Michelle Obama not hug or kiss Berlusconi, but in here lukewarm handshake, she extends her arm to it's full length - rather than with bent elbow ( about 100 - 120 degrees would have been much better and is a good norm for business in most countries) and a closer torso/whole body and thus a more sincere greeting. Silvio is obviously displeased and the President, with expected emotional dissonance, is caught in the middle.
There are many often overlooked components to a successful handshake and this is only one. Michelle (probably?) knew the message she was sending here, and she was very deliberate about it. But on the World's stage it is easy for us to see this frozen image and dissect it in retrospect. In real-time however - in our own spheres of business, law, medicine, sales and diplomacy of a slightly less grand scale - simple mistakes like this - result in distancing (and lost opportunity) of much more than that of a greeting. This is particularly important in conducting business with those from a city, country or culture where this (and other maneuvers) would be viewed as very cold and aloof (as it is certainly seen from an Italian and Southern European point-of-view). Perhaps the first lady thought she was sending a more subtle message? I think this is a fair bet.
We are fundamentally emotional beings wearing thinly veiled intellectual and logical costumes. Never discount or minimize the emotional components - for they are the true drivers for everything else. The opportunity to touch another human being is so incredibly important. We are very foolish to squander it.