22.24Where backdoor dominant comes from

Think of borrowed harmony from C minor.

In C minor:

iv = Fm

A common borrowed movement in C major:

Fm → C

Now extend that idea:

Fm6:

F A♭ C D

B♭7:

B♭ D F A♭

Notice how related these are.

B♭7 shares:

D F A♭

with Fm6.

So backdoor dominant is closely related to borrowed iv/minor-plagal harmony.