Like a Pringles vendor sounding an alarm about obesity, Pope Francis fashioned himself a feminist last week.

You are not reading The Onion.

It was an epic mismatch of messenger and message, and I say that as someone who is thankful for this pope, admires him greatly and believes that a change of tone even without a change in teaching has meaning and warrants celebration.

But a change of tone in defiance of fact should be flagged (and flogged) as such. And neither Pope Francis nor any other top official in the bastion of male entitlement known as the Vatican can credibly assert concern about parity between the sexes. Their own kitchen is much too messy for them to call out the ketchup smudges in anybody else’s.

Francis actually went beyond concern. He vented outrage, calling it a “pure scandal” that women didn’t receive equal pay for equal work.

He left out the part about women in the Roman Catholic Church not even getting a shot at equal work. Pay isn’t the primary issue when you’re barred from certain positions and profoundly underrepresented in others.

Pay isn’t the primary issue when the symbolism, rituals and vocabulary of an institution exalt men over women and when challenges to that imbalance are met with the insistence that what was must always be — that habit trumps enlightenment and good sense.

Let’s be clear. For all the remarkable service that the Catholic Church performs, it is one of the world’s dominant and most unshakable patriarchies, with tenets that don’t abet equality.

For women to get a fair shake in the work force, they need at least some measure of reproductive freedom. But Catholic bishops in the United States lobbied strenuously against the Obamacare requirement that employers such as religiously affiliated schools and hospitals include contraception in workers’ health insurance.

Never mind that only a small minority of American Catholics buy into the church’s formal prohibition against artificial birth control. Some Catholic leaders don’t merely cling to that hoary stricture; they promote it, despite its disproportionate effect on women’s autonomy.

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?

Isn’t it more important that there be enough priests to bring the Eucharist to Catholics than that all those priests be men?

Can the church afford to alienate a generation of young women mystified by its intransigence?

“They’ve grown up in a world where all doors have been open to them,” said Kathleen Sprows Cummings, director of the Cushwa Center for the Study of American Catholicism at the University of Notre Dame. “And it just strikes a disconnect when they see the church with no female leadership — at least they’re not the ones at the altar.”

Francis hasn’t sanctioned any discussion of putting them there. When pressed about that by an Italian reporter last year, he reminded her that “women were taken from a rib.”

Was he ribbing her? He laughed and said so. But the metaphor remains, and it casts women as offshoots, even afterthoughts.