It’s good to be the CEO of IBM at the Augusta National Golf Club. The annual host of the Masters Tournament has offered membership to the last four CEOs of its top corporate sponsor. Donning the club’s legendary green jacket has given these executives the opportunity to play and network with a powerful and exclusive membership body that includes Warren Buffet, Bill Gates and Jack Welch. Ginni Rometty, the company’s new top dog, has been granted no such honor.

Unfortunately for Rometty, she falls one Y chromosome short of Augusta’s membership requirement.

Augusta’s no-girls-allowed policy places it at risk of losing IBM’s major sponsorship dollars. The decision not to offer Rometty membership has turned into a high-profile public snub that has even attracted a finger wag from President Obama. It’s worth noting that even the president wouldn’t have had a chance to play the hallowed fairways until 1990, the year the Club admitted its first black member. It’s difficult for me to appreciate that in my own young lifetime, African-Americans were actually excluded from membership.

Now, just as then, Augusta National is on the wrong side of history. The club’s embarrassingly outdated policy serves as a link to the worst kind of past. The troubling case of Ms. Rometty presents an opportune moment for the Club to escape its tradition and all the high-profile criticism that surrounds it. Unfortunately, such convenient endings rarely accompany these sorts of tales.

As reported by PBS in 2002, former Augusta National Chairman Hootie Johnson was quick to point out that as a private organization, the club maintains the right to set its own membership policy (however discriminatory). From a legal perspective, Mr. Johnson is clearly correct. But his position is difficult to defend on principal. He maintains that the club’s single-sex policy is in line with other cherished American institutions such as “the Boy Scouts, the Girl Scouts and countless others,” the report said.

This claim is a little alarming. There are a number of obvious reasons why the Boy Scouts do not admit women. Out of respect for Mr. Johnson, I won’t bother enumerating them. Augusta National, in contrast, is a golf club. There is simply nothing about the experience of playing recreational golf that lends itself to complete gender segregation.

Of course, Augusta National is much more than a golf club — it’s also where some of the world’s most powerful leaders go to mingle. This function, however, makes its exclusionary policies even more disturbing. By barring women from an arena of major political and business discourse, it promotes an archaic boys’ club image of both athletics and leadership.

It might be possible to simply roll our eyes at this antiquated policy if Augusta National were any other golf club. But it’s not. Augusta National hosts the Masters — the first and perhaps most popular of the men’s four major championships. Its position in the public spotlight (a rather lucrative one) makes its discriminatory policies intolerable. Among the tournament’s tens of millions of annual viewers are aspiring female golfers, business leaders and citizens. Augusta National has a responsibility to project an image consistent with 21st-century society.

Perspective takes courage. Leading social change requires extraordinary strength. No one, however, is asking the Club to exhibit such courage or strength. We simply ask that Augusta National catch up to the rear of the pack. There comes a time in the life of all social institutions when they are asked to change in order to accommodate the advance of social paradigms. I fear these institutions too often convince themselves that “it’s more complicated than that.” And too often, it simply is not.

Augusta National is clinging to a past that should not be celebrated. The Club was wrong to reject black membership just 25 years ago, and it is wrong to reject female membership today. I’m afraid history will remember both policies as equally absurd. The Club now has a golden opportunity to save its image by celebrating an offer of membership to Ms. Rometty. But I won’t hold my breath.