Given two sinusoidal signals of amplitude \$V : A = V sin (\omega t + \phi_1) \text{ and } B = V sin (\omega t + \phi_2) \text { where } \phi_1 \neq \phi_2 \$ we would say that we were presented with two phases. The phase angles are different.
Why is this a special case when \$ \phi_1 \neq \phi_2 \text{ and } \phi_1 = 0, \phi_2 = \pi\$?
Vectors with exact opposite direction (180 degree phase difference), so that they are parallel to each other, cannot define a 2D space, only 1D space, and as a result, they cannot provide rotational vector, so such system cannot be used to produce a decent motor.
Or, looking it in different way, you can
always create the inverted (180 deg shifted) waveform. A single-phase motor does this; some of the windings are wound in opposite direction, providing the 180 deg shifted pole of the pole pair. A full-bridge rectifier also does this.
Even a 3-phase motor does this; the minimum practical number of poles is 6 (for a 3-phase, 2 pole (= 1 pole pair) motor), and of each pole pair, one of the pairs is inverted.
So a single phase system easily allows generation of 0 deg and 180 deg vectors, wherever you need them, doing it earlier at the transformer adds no value compared to doing it at the motor. (Actual phases with phase shift not 0 or 180 deg
can be generated by LC circuits, provided by run/start capacitors with single phase motors, and once the motor is running and storing momentum, a truly single-phase pulsating 1D vector can provide some torque with high ripple to keep it running.)
So a 180deg phase shifted second "phase" does not provide anything which already isn't available with a single phase wire. That's why we don't count it.
A "real" 2-phase system has the phase shift of 90 degrees; motors can then provide 0, 90, 180, 270 deg poles by choosing the winding direction per pole. This defines full 2D space and allows a true rotational torque vector. Such 2-phase systems are almost non-existing but we mentally use them to model 3-phase motors.
So yeah, we
could define word "phase" in whatever way we want, for example, an imaginary 5-phase system could have the following phase shifts: 0 deg, 0 deg, 0 deg, 0 deg, 0 deg. But as a
practical result, it would be identical to the single phase system.... just like systems that contain phases with +pi rad offset to already existing phases. These phases are not very useful. Hence, we talk about split-phase instead of 2-phase, and leave the term "2-phase" for the "true" 2-phase system with 90 deg phase shift.
Stepper motors are the most widely used case of 2-phase power system, although that may not be obvious to anyone looking at them first. When you microstep a "bipolar" stepper and look at the waveforms, you start to understand what's happening.