And how does their vilification of the Leadership Conference of Women Religious, an organization that represents 80 percent of American nuns, square with women’s equality? In 2012 the group was denounced by the Vatican and put under the control of three bishops charged with cleansing it of its “radical feminist” inclinations, including more attention to the poor than to sexual mores.

To his credit Pope Francis declared a truce with the nuns just last month. Also to his credit, he has signaled sympathy for women trying to limit the size of their families and has urged church leaders not to get too caught up in issues such as abortion and same-sex marriage.

And the trend line in the Vatican and in Vatican City government is apparently toward a greater number of female employees, though in 2014, according to The Associated Press, they held less than 20 percent of the jobs. That needn’t be the case, even factoring in women’s exclusion from the priesthood.

But the church’s refusal to follow some other Christian denominations and ordain women undermines any progress toward equality that it trumpets or tries. Sexism is embedded in its structure, its flow chart.

Men but not women get to preside at Mass. Men but never women wear the cassock of a cardinal, the vestments of a pope. Male clergy are typically called “father,” which connotes authority. Women in religious orders are usually called “sister,” which doesn’t.

And things could be different. Traditions change. History and mythology yield to fresh interpretation.

Yes, the Bible says that all 12 of Jesus Christ’s apostles were men. But I’ll see you that dozen and raise you one Mary Magdalene, to whom Jesus supposedly appeared first after the resurrection. Isn’t her role as foundational to the church’s birth?