Oh, I'm flexible and adaptive enough to accept anti-phase. Or we can go with bushels per acre if my acceptance is not acceptable.
As anti-phase, this how Van and Vbn appear when measured on a common time base.
Neither I, nor Jim, nor Rick, nor Rbalex, nor any of several others have disagreed that, to use your words, the two legs appear to be in anti-phase on your scope. Neither do I, and I presume the others as well, disagree that it can be used in that manner for many, many purposes. And as Mivey and I finally came to agreement in a prior thread, unless there is a compelling need to understand otherwise then feel free to call them opposing phases.
The question on this thread was "Why is residential wiring known as single phase?". The question was undoubtedly asked for the same reason you keep defending, and no one is really questioning. When metered or scoped it appears to be two opposing phases. And when used it works like two opposing phases. So why, when it quacks like a duck and looks like a duck is it not called a duck?
To properly answer the question you have to investigate the things that make single-phase different from two opposing phases. There are real differences. But your scope setup will never show them. The test I gave you in the prior post establishes a different time base. It shows a different result. It demonstrates that when you change test conditions then you see different results. But the question isn't "What does residential wiring appear to be?" or "How can residential wiring be used?" rather it asks why it's called what it's called.