I think it's because you argued that Captain Kirk committed genocide by taking out the Narada. I've thought of his opening fire is more of a mercy killing than anything. Nero said he'd rather die in agony than accept help from the Enterprise. But letting the ship just tear itself apart isn't exactly merciful.
I know, to be fair, you wanted this topic to return to TUC, which I appreciate, but...
What Kirk does fits the definition of genocide. Not even the definition that I provided, but that which
NCC-73515 did on
the previous page. I think some people get confused and conflate the word's meaning with "total obliteration of a race". It doesn't have to mean that. A partial murder of a race or group still counts. The Romulans aboard the Narada are clearly a race of people, and from the standpoint of the movie's time-setting, pretty unique, since they are from the future. Therefore, Kirk is actively targeting and wiping out a whole group, as small as it is next to the fuller stock of 24th Century Romulans they come from.
I suppose you could interpret it as a mercy killing. But that's evidently not what's on the mind of Spock or Sulu, and I don't know why it would be on Kirk's, either. Nero may be something of a mad dog, and he and his crew may have committed genocide themselves, but it's no excuse for Kirk's actions. It would have been more poetic to leave Nero to his fate -- after all, that is what he wanted. In fact, given that he says he would "rather die in agony than accept assistance from you", it seems like Kirk believes he is helping him have an agonising death, with his smarmy "You got it", right before ordering Sulu to hit Nero and ship "with everything" they have.
Letting the ship tear itself apart isn't merciful, no. But helping it to its death? Moreover, Kirk says just seconds before he is willing to provide help -- so presumably, he could do something other than blow them all to bits. Since people were fond of throwing earlier bits of Star Trek at me, and one of the examples was Kirk bitterly kicking Kruge to his death in ST III, I'd like to point out that Kirk does better with his second-in-command. That guy openly says, "I do not deserve to live", and Kirk misleads him for a second, only to deliberately not grant him his wish: "Fine, I'll kill you later." But not ST 09 Kirk. He -- along with Spock and Sulu -- was perfectly happy to eliminate everyone on that ship. No mercy.