When trying to understand the refraction of light when it hits a slower medium, lots of people seem to be enlightened by the 'marching band' or 'marching soldiers' analogy, which 'explains' that when a platoon marching in a straight line on a concrete road hits the side of the road at an angle and goes into a swamp, the soldier which is first to hit the swamp will start walking slower while the soldiers that are still on the road keep going at the previous speed. This supposedly explains intuitively why the marching band changes direction.
I don't understand how this works at all, the soldiers hitting the slower medium will start walking slower but why on earth would they change direction as well? As I see it, the front line of soldiers will form a different angle to the direction the platoon is marching in after it has hit the interface, but the platoon should still be going in the exact same direction even if the soldiers run into each other because the guy in front is slowing down. Am I missing something in the analogy or is the analogy a really bad one (which I'm starting to suspect strongly)?