This article supplements Julio Tuleda, Enrique Burguete, and Justo Aznar's “The Vatican opinion on gender theory” (Linacre). It supplements their article by providing a stronger argument for the thesis that “intersex” does not violate binary sex in human beings. In their response to Timothy F. Murphy's criticism of “the Vatican's” (rightfully corrected as the Magisterium of the Catholic Church's) position on the sex binary, they argue subsidiarily that “intersex” does not violate the sex binary. However, their argument against Murphy as stated is implausible; however, I provide a much stronger argument for their conclusion that intersex does not violate the sex binary. I intend to perform this supplementation in two stages, assuming the reader's familiarity with “The Vatican opinion on gender theory.” First, I provide a broader background than Murphy's to the challenge that “intersex” conditions violate the sex binary, showing both how Murphy's criticism is unoriginal and how “intersex” both has been, and continues to be, misunderstood. Second, I problematize Tuleda’s argument, and offer the strongest argument for the conclusion that “intersex” does not violate the sex binary on purely secular/nonreligious grounds (addressing Murphy's complaint). I conclude that the Magisterium of the Catholic Church remains correct that sex is binary.Summary:Julio Tuleda, Enrique Burguete, and Justo Aznar's “The Vatican opinion on gender theory” challenges Timothy Murphy's criticism of sex binarism as endorsed by the Catholic Church. This article strengthens their criticism by focusing on “intersex” conditions.