Some disembodied voice tells you to go and kill a bunch of massive creatures. So you do. The game's basically saying "do whatever the voices in your head tell you to do". Sure, there's the promise that it will bring your beloved back from the dead (at a price), but how many innocent lives is she actually worth? Most of these huge beasts are just minding their own business and only attack once provoked.
Indeed, Colossus 13 doesn't even retaliate, instead merely attempting to shake you off. And they clearly feel pain - stab them in the head and you'll know about it. Come on, one of them's even got a cool beard, yet you still killed it, didn't you? It's dead now. You did it. Shame on you.
Above: Shadow of the Colossus - an extraordinary experience, with the most palpable sensation of guilt any game has ever given us