Metspitzer wrote:

It is considered single phase. If you remove the center tap, you have
the same thing on the primary as you do on the secondary.

If you chose to put the secondary tap anywhere but the center, you
still have 240 total, but the fraction of 240 changes as you move the
center tap.

This sentence is the one that doesn't ring true.
"The two insulated wires each carry 120 volts, but they are 180
degrees out of phase so the difference between them is 240 volts. "