Almost any situation where we're trying to design a functional solution to a technical problem. I actually used to have a phrase for this: "You can't build a rocket ship with emotions." If my goal were really to successfully build a rocket ship (as noted in the maxim) then I'd be delighted to be proven wrong. Every correction would get us closer to our goal.

Alternately, if someone were interested in empathizing with the team and protecting egos, we might navigate towards a worse solution. One which took into account everyone's feelings, instead of a cold calculation of method and results.

You seem to be conflating "delivering criticim" with "hurting feelings", and I don't understand where that's coming from. Would you be delighted to be proven wrong if for every mistake your boss or peer told you that you were an incompetent idiot who doesn't belong on the team? Would that make you want to do more work? Would that make you feel comfortable proposing an idea that you aren't 100% sure ir correct and already known to your teammates to be correct?

Nothing about respecting teammates and their emotions says you have to accept their pull request.

I think this is a fair criticism, and I agree that if my boss publicly called me out and insulted me, I'd be pretty discouraged. I might not have made my point very well, but I certainly didn't mean to imply that being outright caustic was ok, either. I only meant to say that it's still possible offend and arrive at the wrong decision by employing NVC.

There is no contradiction between the two. You absolutely can emphathize with team and protect egos while also discuss efficacy of solutions or correctness.

It is not even hard. Just keep it factual instead of using words like "stupid", "shitty", "crap" or passive aggressivity. Discuss issues before they become big. Listen when they disagree with your assessment - they might have reasons.

I already met enough people who claim to criticise while actually venting their emotions and settle scores with those they dislike.

That's an interesting maxim. Do you think NASA ran the Apollo program by ignoring the emotions of everyone on the project? If it didn't, should it have?

I just think this is more of pendulum sort of thing. You can go too far in either direction. If I'm erring at all, it's because I've been in circumstances where a complex project suffered due to social agreement.

But for certain, you could go too far in in the other direction: completely ignoring everyone's emotions.

Specifically, if you're in an environment that's swung too hard in the direction of totally ignoring people's emotions, then my advice probably sounds awful.