I suspect that at least part of it amounts to military men obey orders, which people who buy into the stereotype see as a sign of not thinking for themselves and/or not wanting to think for themselves. Add in the general image of 'if you have muscles, you must be one of those obnoxious people who spends all his energy on them instead of on intellectual pursuits' and the assumption that smart people don't want to fight and would find a way to get out of having to do so, and it all kinda stacks up regardless of accuracy.