The authors try to offer a "feminist" reason for doing so:
Authentic sexual equality requires that men understand with their bodies (as women do) the procreative potential of the sexual act. And this is exactly what natural methods of family planning do. By frequenting sex only during infertile times when a child is unwanted, men learn to coordinate their desires for intimacy with the natural rhythms of the female body. Feminist scholar and theologian Angela Franks notes that “[this] is unheard of in a society in which male desire appears to set the guidelines — especially in the ‘hook-up’ culture. Indeed, such a reorientation ofdesire is more revolutionary than any secular feminist project.” Those who practice this approach to family planning report that its use tends to make husbands more sensitive to the sexual and emotional needs of their wives — a sensitivity that many women have long found wanting.I'm going to admit here that my sexual experience isn't widespread: My bachelor years weren't all that swingin'. So maybe I'm going to sound stupid here. I'll risk it.
But my limited experience tells me that a woman's desire for sex often (but not always) peaks around that time of month that they're most fertile. (Evolutionarily, this makes sense, no?) And my limited experience also suggests to me that desire for sex and enjoyment of sex are somewhat related. If you're not in the mood, you're not in the mood.
All of which is a roundabout way of saying: National Review's writers apparently believe that men can best practice birth control and respect women by having sex during those periods in which women will desire and enjoy it least. "Be attentive to the sexual and emotional needs of your wife, men: And then do the opposite!"
Put aside the questions of whether the rhythm method is all that effective. A big problem here is that National Review's authors essentially remove a woman's sex drive from this equation. No surprise there, I guess. If you believe that a big problem with contraception is that it enables women to act on their own sexual desires (and the authors clearly do) this proposed solution makes a lot of sense.