> Why is North American residential power called single phase?

Because that's exactly what it is.

Utility power in North America is distributed via single-phase transformers with their primaries being fed 12.47 kV using 2 lines of a three-phase system or 7.2 kV using a line and neutral.

The distribution transformers, which are pole-mounted, are also known as a 'pole pigs'. 

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The single secondary winding L1 - L2, with an earthed centre tap designated as the neutral, provides a single-phase 240 V supply between L1 and L2 and two single-phase 120V supplies, which are out-of phase by 180°, between L1 & N and L2 & N. 

Hence it is referred to as a 'single-phase, three-wire' system or 'split-phase' system. 

> I am under the belief that North American residential power is a special case of two phase power adequately described by the term split phase.

> A theoretical explanation seems to require a unique definition of phasors or to define our electrical system by the loads we attach rather than the voltage source supplying the current with a zero point reference.

A single-phase alternator, has a single winding that produces a single, continuously alternating voltage.

A two-phase alternator, now obsolete, had two windings spaced 90° (electrical degrees) apart with the voltages generated in them having 90° phase displacement.

A three-phase alternator, has three windings spaced 120° apart with the voltages generated in them having 120° phase displacement.

A single phase induction motor, having two windings spaced 90° (electrical degrees) apart is actually a two phase motor. The single phase supply is split into two phases that are out of phase by 90°, by connecting a capacitor in series with one winding. A single phase induction motor is hence referred to as a split-phase motor.

The single-phase, three-wire system, with its two voltages being out of phase by 180°, does not qualify as a two-phase system.

  [1]: https://i.sstatic.net/pZKEw.png