Interesting topic.
It's actually only one phase. The wiring results in opposite polarity, which is not a different phase.
https://www.prosoundweb.com/phase-polarity-causes-and-effects-differences-consequences/
Note in the pics below, the input side of the transformer is only one line - i.e. one of the three phases available from the transmission lines. What you do not have are two different AC signals in that secondary coil.



Three phase is for transmission only. You only get one phase to a house. Three phase provides constant power (DC) even though Voltage and Current are AC. That's the mathematics of having three signals 60 degrees apart.
Here's a site with a lot of nice pole pics with varying connection types for 3 phase.
http://waterheatertimer.org/How-to-identify-transformer-wiring.html
Ah, yes. Old brain, new tricks. You get multi-phase through additional expense or a rotary converter. Its the 480 volt (and up) users who get three phases.
Oops, three signals 120 degrees apart, not 60.
It’s 180degree two-phase into your house at your box. You are correct that it comes from only one of the three phases off the utility line, but the diagram you show CLEARLY shows that it’s 180-degree 2-phase coming out of the transformer - those three lines - the neutral and the two other phases are the three lines that come into your home. Code additionally requires you to supply a true ground/earth line, for four unique conductors in your breaker box. But that transformer is NOT in your house and you are NOT directly connected to the single phase of anything. The secondary coil separates you from the main utility line and that secondary coil provides you with 2 phases and a neutral.
It is technically wrong to say you have “one phase 180 degrees out of phase with itself.” Those are two different phases off the same coil, that’s fair to say, but they are different phases.
As I said earlier, most of your outlets are 110V/120V and wired across ONE of the TWO phases and the neutral. The ground line is taken to all of those outlets as well, which is why you have three wires in those boxes. Your 220V/240V outlets for your dryer or other tools has both phases, the neutral, and the ground wire in the boxes.