President Obama is in a flap. His administration, like the movie The Hobbit, doesn’t have enough women in key roles. The last three White House staff announcements have featured the following people: John Kerry, Chuck Hagel, John Brennan and Jack Lew. All white dudes.

The New York Times energized elite conversation on this topic with a photograph on the front page of Wednesday’s paper. In it Obama addresses a semicircle of 10 male aides and Cabinet officials (the coalition of the besweatered). They are arrayed in precise formation, as if to block out senior adviser Valerie Jarrett who is barely visible in the picture. (She is so hard to find, CNN used a special shading to identify her leg.)

The president’s men are irritated by this criticism. The focus on this momentary snapshot, they argue, ignores the more complete picture. If that is so, they have only themselves to blame.

During the campaign, the president and his allies took every opportunity to pander to women voters, and never let a moment pass — whatever the pretext — to draw broad conclusions about Mitt Romney’s lack of concern for women. When a Romney aide didn’t have an immediate answer about the candidate’s position on the Lilly Ledbetter Fair Pay Act, it was portrayed as a dire sign.

It wasn’t just Romney’s shortcomings that created the conditions now bruising Obama. The rapid twitch to all things related to women and the relentless courting created a supercharged political atmosphere. When Hillary Rosen, a Democratic strategist unrelated to the Obama campaign, made a clumsy remark about Ann Romney “never working a day in her life,” Obama’s top strategist David Axelrod and campaign manager Jim Messina denounced her immediately so as not to offend women.

The most unintentionally hilarious moment came at a White House forum on women and the economy. The event was intended to show women voters, who are particularly sensitive to the weak economy, that the president cared about them. The forum was clearly treating women as an interest group. So, it was chuckle-worthy when the president declared, “Women are not an interest group.”

Since re-election, the Obama administration has not shrunk from playing the gender card. White House officials repeatedly asserted that U.N. Ambassador Susan Rice’s critics were only beating up on her for Benghazi controversy — and not the president or the CIA Director — because she was a woman. That is what the president appeared to be suggesting when he said Republicans were picking on Rice because she was an “easy target.”

If people are now drawing grand conclusions based on a few staff picks, it’s because the Obama team helped train them to do so.

The recent staff picks also link with a critique that has some validity. We’ve heard since the early days of the Obama administration that the inner circle has a male bias. We know this: If Barack Obama were facing a third election at least one of his top players at State, Defense, or Treasury would be held by a woman. Needing suburban women voters, the president just couldn’t afford to have a Cabinet where one of the faces most likely to be in the news cycle every day was not a woman.

But let’s not go overboard. The power of symbolism needs to be balanced against the practical effect of that symbolism. To put it into perspective, as my Slate colleague David Weigel pointed out, let’s imagine John McCain had won in 2008. We would have gotten to know Vice President Sarah Palin! And the policies she supported would have been far different for women than those supported by Obama and Vice President Joe Biden, who drafted, for example, the Violence Against Women Act.