The framers were very careful in how they structured the new country, as we all know.  There was a great fear of standing armies at the time, because it was believed that a standing army would be a constant threat to the civilian government's control of the country.  As a result, the office of POTUS, created by Article II (that's right, Congress is more important than POTUS according to the framers), was placed as the ultimate authority over the military.  This was to ensure that the military would only serve as a tool of the civilian government and not as a separate power center.

The wisdom of this approach has been proven many times over, as numerous countries around the world have fallen under control of a military junta while the civilian government has been removed from power (e.g. Pakistan).  The idea that being a military man is a desired quality in a president is thus laughable in my regard, except that so many people seem to believe it.  Note that we have had precisely two Generals (though numerous lower level former military) serve as presidents, and both were subpar, IMHO.  And in order to ascend to the presidency, it is a REQUIREMENT that a military officer resign his commission, just as a sitting senator must vacate that seat to ascend to the presidency.

In other words, YES!  The CinC meme is insane!