No.
There is no 180 phase shift.Your own oscilloscope proves that using the waveform math because if you sum those waves you put up the result is zero volts.
The oscilloscope picture plainly shows two waveforms that are 180° out of phase. When one is at the voltage peak with respect to the reference (which is ground) the other is at the voltage minimum with respect to the reference. The voltage at a point is the potential difference between that point and some reference point. The potential
difference (voltage) between two points is the difference in the potentials measured with respect to a common reference. In this case at peak we'd have +120 (ignore the sqrt(2)) factor on one phase and -120 on the other both with respect to the neutral. They are out of phase and the difference in potentials is 120 -(-120) = 240V. That's how this works. Subtracting the waveforms on the scope proves nothing except that they are (if I get a flat line) equal and opposite in phase (as they should be). Try to understand this. If you don't fully appreciate how voltages are measured it is little wonder you are confused.
The only reason it looks like they're 180 out is because you're using the wrong reference point. A parlor trick, for lack of better terms.
There is no such thing as a 'wrong' reference. The choice of reference is completely arbitrary as long as it is common. You may not like my choice of reference because it shows the fallacy in your argument but there is nothing wrong with it. If I choose the physicists reference, a sphere in space infinitely far away, there may be a cajillion volts potential difference between that point and the center tap on the transformer but that doesn't matter. When the potential at the top winding termination goes up to a cajillion + 120V the potential at the bottom winding will go down to a cajillion -120 and the difference will be 240.
And your choice doesn't change things either. With using the bottom phase as the reference you get +120 to the center tap and +240 to the top. Thus the potential across the top coil is +120. Thus the bottom is at -120 with respect to the center tap and the top at plus 120. Same as before.
If the choice is arbitrary then which point should we pick given that we can get the same information from any? I'd say the one that makes things the simplest. It seems obvious to me that in a balanced system with the center tap earthed ground (or the grounded conductor) is the obvious choice. When examining the wave form from an outlet on either side of the panel the reference is available to us. If we used a phase for the reference we'd have to drag a wire across the floor if the reference phase were connected to the opposite side of the system. Of course if all we are interested in is one side we can use that side's phase as the reference. Using the neutral produces equal voltages when both phases are examined. As the whole object of the system is to have 2 lower voltage circuits this would be desirable.The thing I really like about it is that it is consistent with the notion of the neutral as defined by the IEC as the conductor that connects to the star point in a Y connected polyphase system. IOW you don't have to shift gears when going from 3 phase to 2 phase systems.
One would think an EE would know that two waves of equal amplitude and frequency, when 180 out, will cancel not sum. Since we know the waves aren't canceled when both legs are used, we know the waves cannot be 180 out of phase.
We don't have two generators in series that are 180 apart. They are in phase. But they are connected L1---->T---->L2. Note that the high side (>) of the L1 generator is connected to the T (center tap) as is the low side of the L2 generator. This can be modeled by two generators which are 180° out of phase each with its low side connected to the center tap L1<---T--->L2 and that's what the textbooks and the 3 references mean/show when they diagram or talk about two out of phase sources. In any case L1 and L2 are 180° apart in phase with respect to T. They may do it this way because if you add a third arrow (generator with lo side to neutral) to make a thing that looks like the Mercedes logo you have the phasor diagram for a Y connected 3 phase system.
As this is going to be my swan song here (no point in repeating the same material to deaf ears again) I might suggest, if you know anything about electronics, that you have a look at things like push-pull amplifiers which are really exactly the same circuit with emphasis on trying to understand what the 'phase inverter' is for (in the simplest case it's a transformer connected just like the power pole ones but it can be electronics as well). Balanced mixers are another circuit which uses a center tapped transformer as a phase inverter.
All the spin, fancy dancing, and deflection doesn't change the fact that waves 180 out don't add, they cancel.
That depends on how they are connected. In a differential amplifier such as in a balanced microphone circuit (that's something else you might look at) they add. If you have two generators connected back to back (lo side of each to neutral), as we do here, they add. You
must, when thinking about these things consider both the phase of the generator and how it is connected.
Your problem seems to be mostly caused by inability to recognize that there are other ways to model things than the model you cleave to. L1-->T-->L2 with the generators in phase is a fine model if you use T as the reference and a workable but clumsy one if you use L1 or L2. But L1<--T-->L2 is an equally good model
if the generators are 180° apart in phase (and again you have the choice of reference). It's a better model in that it is symmetrical as is the system it is modeling. Symmetry makes things easier to see (for most people). The results will be the same with either. Voltages measured at L1 with respect to T will be of equal amplitude and opposite phase compared to voltages measured at L2 with respect to T.
Further, the point about being two phase in this case is wrong. I grant you that two phase power could exist and may well exist in the wild (120/208 - 120V L-N, 208V L-L), but what we're discussing isn't that nor is that common household distribution.
Certainly in most cases brewers will be in their homes in the US but the US isn't the whole world and the fact that in most cases it comes from a transformer on a pole doesn't make it wrong. You are still getting two phases. My reason for bringing this up was I thought that if you could understand what's happening in a 120/208 biphase system and appreciated that the only difference between that and the split phase system is 120° vs 180° you would understand that they are really the same in terms of voltages. But that didn't work. I also brought up the zig-zag generator wiring method as a means of obtaining split phase in the hopes that this would help you to see how things work but that didn't work either.
Frankly, I think the whole notion of two waves in this regard (120/240 split voltage) is even flawed. It's the same wave, you're just looking at half of it on the left and half on the right from the midpoint.
I thought you were of the opinion that looking at things with respect to the midpoint was a parlor trick.
No out of phase involved because it's just plain old, simple, single phase.
Once the third wire goes in it is no longer single phase. I will not repeat the definition of polyphase as I getting tired of laying this out for you over and over again. But I will point out that the two waveforms are not exact copies of one another because the transformer is not perfectly symmetric nor is the load. If one side has a power factor different from the other there will even be a phase shift so that you will have a phase difference of something other than 180°. This removes the 'mirror phase' argument but I feel more like a lawyer than an engineer in pointing that out.
If you look at voltages with respect to the midpoint there is no question that one phase will be 180° out with respect to the other (at least in most practitioner's minds).
All the talking point trying to apply polyphase theory are non sequitur.
Charlie Chan said in one of those movies "Mind like parachute. Function best when open." It's disapointing that you can't see the relevance but I don't feel that I've wasted my time entirely as it's sort of fun to go back and review some of this stuff.
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