I don't personally think of corpses as anything special, but for those of us who've been dragged from funeral to funeral, it's hard to say that what I think should be done with corpses should be forced on everyone else.
Consider this-- the corpse is the most tangible reminder of who that person was. While to our soldiers it may be a reminder of a disgusting human being or a war they want to get the hell out of, to the dead person's family that corpse is the only physical thing they have left of their loved one. These people were not terrorists to their families (or so I would hope), they were husbands, sons, fathers, cousins, friends. These were not universally terrible people, so to expect everyone, including their loved ones, to treat them as such is self-centered and moronic.
Back to the corpses themselves. Since the body itself is the best reminder of who the person once inhabiting it was, the treatment of the corpse is often tied to how one would treat that person in life, albeit symbolically (I hope no one would bury or burn loved ones while they're alive
). It really is an issue of respect, not for the pile of dead meat and bones but for the person who once inhabited said pile.
And for those would say "sentimental symbolism is moronic", consider this: we use symbolism EVERY SINGLE DAY. Words themselves are mere symbols; we can't transmit our thoughts to one another directly, so we've manufactured and agreed upon the rules of usage of phonemes and alphabets (in English, mind, not speaking for other languages here) so that we can try our best to communicate what we really think. When we tell people that we love them, do we have a concrete object called 'love' to give to them? No, not really, so it's an abstract idea we've tried to put into relatively concrete terms through language and, hopefully, actions.
Additionally, as someone else already noted, these soldiers did NOT view the bodies as mere hunks of meat. They attributed symbolic meaning to their actions, too. I doubt that these people go about their daily lives pissing on roadkill and ground beef.