Pakistan is so angry at the United States that it’s going to . . . what? The puzzling conclusion to that sentence is at the heart of the latest squabble in the world’s most vexed geopolitical relationship.

The Pakistanis are understandably enraged by last weekend’s border incident in which U.S. and Afghan forces killed about two dozen Pakistani soldiers inside their country. No nation can tolerate such a violation of its sovereignty without making the most emphatic protest.

And that’s what Islamabad has done: In their pique, the Pakistanis will boycott an international conference in Bonn next Monday that will endorse a regional framework for stabilizing Afghanistan. That conference is one in which the Pakistanis might have played a crucial role (and made some new friends), but they’re staying away.

The Pakistanis have also closed the two main land-transit routes for supplying U.S. forces in Afghanistan. Gen. John Allen, the U.S. commander in Kabul, says he has enough extra supplies to cope, but for how long?

The key resource is fuel. My guess is that if the passes stay closed for four to six weeks, the United States will have severe problems maintaining its operations.

You can fly in a lot of supplies via the Northern Distribution Route that transits Central Asia, but you can’t airlift tanker trucks. So what happens when U.S. military equipment stops moving in Afghanistan? Would a hasty American exit really benefit Pakistan?

Pakistan’s expressions of anger aren’t surprising, especially for a military that needs to shows the public it’s in charge, after the humiliation of the May 2 U.S. raid that killed Osama Bin Laden. But do these actions—staying away from a peace conference and closing the border--really suit Pakistan’s strategic interests?

Continued Pakistani reprisals make sense only Islamabad is heading toward a real and lasting break with Washington. I don’t get the sense that’s what Pakistani leaders really want. If that’s right, then they need to figure out how to climb down the hill, now that they have forcefully planted the flag.