The answer from the link said 'in-phase cancellation' which isn't really a 'thing' nor accurate. He was just trying to say that when the signals are in phase you wouldn't get sound. There isn't actually any cancellation going on here. When the signal is the same in both channels there is just no voltage across the speaker so it doesn't do anything.
Their signals are cancelling out because they are in phase, this is a thing. It describes what is happening and why. You are arguing semantics here more than a technical point here, from my perspective. I agree with the physical reason, just because it is simple does not mean you cannot have a term for it in the case.
I am in a way arguing semantics because I believe its confusing to non EE people reading this to use a term like 'phase cancellation' in a way that is very different from its usage in almost every other context. In general it refers to the sum of two waves equaling zero (or some reduced value), i.e. destructive interference. In this case the opposite is happening and the vocals are removed not due to a sum of the waves but rather a difference equating to zero.
Yes, we have interacted there a few times. I would probably use the term "common-mode cancellation." But it is something that is a very base concept in EE and the other terminology makes sense to me, although for non-EE I could see the issue.
You should make hacker news your website on EE? Your account looks some bare there, add some information!
There is no phase inversion here. When the signals are the same there is just no voltage across the speaker. Think of it as putting 5 volts on both sides of the speaker, the voltage difference from one side of the speaker to the other is 0 volts, so no current flows and the speaker is at rest.
(I'm rusty at this, but when I read 'phase', I think of a time difference between two signals. In this case, there's no time difference.)