The colors falling to the ground does terrible damage to the morale of the troops fighting, so keeping them high in the air could potentially have a great affect on my mission, the safety of my comrades, and ultimately my country, so on. If the bearer of the colors were to perish, I would rush to the colors and get them back in the air. This is not really practiced today in battle because there are not large conventional forces facing each other like in the past, but all soldiers understand that letting the flag touch the ground is a very serious insult, because generations of soldiers before us have literally sacrificed their lives in order to keep the colors held high in battle. In battle, banners have been carried for millennia as a focal point to mass troops around, and there is a great amount of emphasis placed on keeping that banner high and visible so your troops can see it from a distance, and know that our fight continues.
Part of the reason this offends so many is because many of us have served in our nations' militaries.
To clarify: there are no laws against burning a flag in the US.