Spock never gives a reason for his objection (presumed, and for that matter it didn't sound like a very strong objection to me). "What are you doing?" It could be anything. It could be practical (they're all about to get sucked into a black hole, and almost did because they wasted time firing torpedoes). It could be political. It could be personal. If it's personal it lacks conviction because of the way he delivers his next line. He never says what he's thinking. If there's nothing there there's nothing there. You fill in the cracks and make up your own reason.
The AbramsTrek future is actually worse than today? This is the first time I've heard that, so I'm just making note.
I agree though about not killing all of Nero's crew if you can help it (even though I sort of practically doubt any of them were innocent, given they all would have known the sheer magnitude of what they're leader was doing. It's not like covering your ears in a Bajoran labor camp). And firing the torpedoes seems a bit excessive every time I watch it.