I remember thinking, ‘what was the most important occasion in the Doctor’s life?’ Obviously it was the day he blew up Gallifrey. Then I tried to imagine what writing that scene would be like, and I thought literally – there’s kids on Gallifrey and he’s going to push the button. He wouldn’t. He wouldn’t. I don’t care what’s at stake, he’s not going to do it. So that was the story – of course he never did that. He couldn’t have. He’s the Doctor, he’s the man who doesn’t do that. He’s defined by the fact that he doesn’t do that. Whatever the cost, he will find another way. So it had to be the story of what really happened that he’s forgotten. Of course he didn’t! He’s Doctor Who. He doesn’t do things like that.” - Stephen Moffat
I always felt The Doctor BECAME a man who “wouldn’t do that” specifically because he was a man who did. Knowing the cost made him into someone who would zealously try anything else first. He didn’t start out that way.
The Fourth Doctor killed Sutekh, last of the Osirians, in Pyramids of Mars (1975) and helped in the genocide of the Pescatons (audio, 1976) in addition to three other occasions. The Sixth Doctor wiped out the Vervoids in Terror of the Vervoids (1986) which was later used as evidence in season 23, The Trial of a Time Lord.
But ultimately, it’s more correct to say he became a man who would never want to do that, placing him in direct opposition to the Time Lords toward the end of the Time War (The End of Time). Because he does “do that,” and continues to.
As the metacrisis Doctor, he tries to eliminate the Daleks once again (though failing as we discover later). There is a little-talked-about parallel between Dalek Caan and the now-revealed War Doctor when he urges the metacrisis Doctor to destroy the Daleks, saying, “No more!”
Going back to The End of Time, the Tenth Doctor sends the Time Lord President (Rassilion, if I’m remembering correctly) and others back to the last day of the Time War, knowing he will seal their fate and condemn them and the other Time Lords to death once more. That’s a second genocide of his own people. They were prepared to tear the Time Vortex apart and destroy the universe, becoming non-corporeal beings.
And then I think about the Star Whale. The Eleventh Doctor was ready to commit a mercy killing that would equal a genocide because he thought he was out of options. The only reason he didn’t is because of Amy Pond’s interference.
So he remains a man who absolutely would do that - but only under certain circumstances. In Journey’s End and The End of Time it was solidly for the greater good of the universe. In the case of The Beast Below, it was mercy. And when the human race received the post-hypnotic suggestion to kill Silence on sight; the Eleventh Doctor gave them a choice: avoid Earth and humans or be exterminated. Surely Silent “children” exist. The threat of genocide stands.
In retconning the destruction of the Time Lords and Gallifrey in order to have the Doctor not “do that,” Stephen Moffat deeply misinterprets who The Doctor has become and strips away a huge amount of character development over the last 8 years, not to mention the moral impact on the viewer.