By David Ignatius

WASHINGTON -- What went wrong for the U.S.-backed government in Yemen and what are the consequences for counterterrorism operations there against al-Qaeda's most dangerous affiliate? Both questions have disturbing answers.

President Obama touted Yemen just last September as a country where the U.S. "successfully" was "taking out terrorists who threaten us, while supporting partners on the front lines." Some administration officials feared Obama's boast would haunt him, and sure enough, just over a week later, Shiite rebels from the Houthi movement seized the Yemeni capital, Saana.

Last week, after four months of relentless pressure from the Houthis and the collapse of his military, President Abed Rabbo Mansour Hadi resigned. Yemen became another shard of the splintering Middle East. The two most powerful forces, the Iran-backed Houthis and al-Qaeda in the Arabian Peninsula, are both strongly anti-American.

What happened in Yemen is not very different from the stories of other Arab nations shaken by the "Arab Spring" revolutions. Armies that had seemed strong under authoritarian rulers crumpled against insurgents. U.S. military intervention hasn't checked the disintegration, nor has American retreat. The conclusion is so obvious we sometimes overlook it: This history is being written by the Arabs, not outsiders. Foreign assistance can help strong, broadly based governments, but not fragile, polarized ones.

Yemen looked like a place where the U.S. had learned lessons from the disastrous 2003 Iraq invasion. The U.S. wanted to replace a corrupt dictator, Ali Abdullah Saleh, but the deal to install Hadi in February 2012 was brokered by the regional powers of the Gulf Cooperation Council. America offered military help, but with the light footprint of special forces, rather than an Iraq-style occupying army. The U.S. sought compromise through a "national dialogue" and a U.N.-sponsored constitutional process.

All good ideas, but the result was the same unraveling as in other weak states. Hopes for dialogue crashed against the realities of weak governance, cronyism, and decades-old sectarian and tribal feuds.

Denis McDonough, the White House chief of staff, betrayed the administration's deep frustration when he admitted last Sunday: "We cannot be an occupying force in a place like Yemen or Syria in the hope that we will be responsible for bringing this, as you say, 'chaos,' to an end."

What happens to U.S. counterterrorism efforts against AQAP, now that our Yemeni partner has collapsed? The answer is that the U.S. will rely on "direct action," meaning drone strikes, even though it no longer has the consent of the host government. U.S. special forces are still embedded with some elite Yemeni units outside the capital. But with a reduced flow of intelligence to feed the drones, targeting inevitably will be less precise -- and the risk of killing innocent civilians will be higher. That's a vicious cycle in the making.

The administration's strategy, strange as it may sound, is more of the same: U.S. officials believe, correctly, that real progress won't be possible in Yemen without a new government that reconciles the Houthi minority with the dominant Sunni population. So they seek dialogue, inclusion, a new constitution -- the same mix of lovable but distant reforms America has favored since 2011. In the short run, policy is driven by one of those amoral Middle East syllogisms: America and the Houthis both hate al-Qaeda, so maybe we can work together.

What's the lesson of this case study of America's frustrated hopes for stability? I can offer a well-researched answer by analysts at the Rand Corp. Simply put, their conclusion is that the U.S. strategy of security assistance doesn't seem to work in the frail Arab states that need it most.

These distressing findings appear in a recent report for the Army, titled "Assessing Security Cooperation as a Preventive Tool." Analyzing data from 107 countries from 1991 to 2008, Rand found that security assistance, a la Yemen, "was not correlated with reduction in fragility in states that were already experiencing extremely high fragility." Such help "is not sufficient to stave off instability," because weak states can't absorb the aid, Rand found. That problem was especially pronounced in the Middle East and Africa.

The best results, the Rand experts noted, came from "non-materiel aid, such as education, law enforcement and counternarcotics." Rand explained that this finding "supports the general idea that investment in human capital has large payoffs."

So that's the painful takeaway from this latest Middle East reversal. Arming weak states such as Yemen doesn't make them stronger. This is a long war where the best weapons may be books and judges.