[
Edit, 9 Jan 2018: The following is not my final position on the matter, but rather a beginning point for working through some thoughts; see further posts below.]
Regardless of whether male headship is legitimate, this passage of Shipley's doesn't get us there — its logic is formally invalid. Given P = "polygamy is legitimate" and H = "male headship is legitimate," the arguments (in order) can be symbolized this way:
P ⊃ H ∴ !P ⊃ !H
and
P ⊃ H ∴ H ⊃ P
Translation of the first argument: "If P then H, therefore if not P then not H" or, in plain English, "If polygamy is legitimate then so is male headship, therefore if polygamy isn't legitimate then neither is male headship."
That's like saying, "If it's raining the street is wet, therefore if it's not raining the street can't be wet" (to use the textbook example). A street can be wet for a number of non-rain reasons — sprinklers, an open hydrant, flooding, copious dew, a broken water main. Although a wet street
may have been rained upon, logic alone isn't enough to tell us so.
Likewise, other premises may lead us to conclude that male headship is legitimate, therefore denial of polygamy need not amount to a denial of headship. It would depend on factors not mentioned in Shipley's syllogism.
The second argument is a variation of the first, and just as invalid: "If polygamy's legitimacy implies that of headship, then headship's legitimacy implies that of polygamy."
So Shipley's conclusion isn't necessarily wrong, but the logic he used here is messed up. It's not a good paragraph to quote in support of one's case — unless your point is that supporters of polygamy are sometimes illogical.