LONDON — Of all the promise of the Arab Spring — for citizenship and agency in the lives of peoples long subjected to servility and humiliation — perhaps the greatest was the idea that the region could escape the paralyzing political trap that offered Western-backed dictatorship or radical Islamism as its only alternatives.

For decades, since the Iranian Revolution of 1979, the Middle East has been caught in this crippling vise. All the ousted strongmen, from Hosni Mubarak in Egypt to Tunisia’s Zine el-Abidine Ben Ali, were insistent that only they stood between their nations and jihadist takeover. This was the currency of their argument to the West. From Washington to Paris, the appeal worked. Money and backing flowed.

In fact, of course, these repressive Arab societies — so illustrative of Western hypocrisy in their power structures, so deadening to the hopes of the young, so shot through with nepotism and cronyism, so distant from a glimpsed modernity — resembled factories for militant Islam rather than bulwarks against it.

When the only place to gather is the mosque, when “secular” equals Western-backed dictatorship and when “elections” amount to a rigged farce, the consolation of the Islamist cause grows. It was not for nothing that Al-Qaeda flourished in the incubator of Arab despotisms, nor that Mohamed Atta, a leader of the 9/11 attack, issued from Mubarak’s Egypt.

In Tahrir Square in 2011, at the time of the uprising, nothing was more uplifting than seeing Westernized Egyptian liberals and the Muslim Brotherhood make common cause in the idea of citizenship based on equal rights for all. Here, it seemed, lay the possibility — however fragile — for the largest Arab society to escape the tired, deceptive secular and Islamist labels and so open up the possibility of a representative and inclusive society.

It was not to be — and this failure will have devastating consequences, inside and outside Egypt. Islamist ire has been fed and the perception of Western hypocrisy reinforced at the very moment when ways out of this impasse appeared possible.

In fact the violent splits nurtured over decades under Mubarak — Westernized liberals against backward Islamists — proved insurmountable. By last month, just a year after the nation’s first free election brought the Brotherhood’s Mohamed Morsi to power with 51.7 percent of the vote, millions of decent Egyptian liberals were roaring in the streets for the military to oust him. The army obliged in the July 3 coup that will not speak its name.

Now the Saudi-backed Gen. Abdul-Fattah el-Sisi, Egypt’s military leader, rails against “the terrorists” who (he insists) constitute the Brotherhood, and has his newly subservient media echo the refrain. More than 1,000 Egyptians are dead. There is talk of banning the Brotherhood; certainly its participation in any future election is impossible to imagine. In its absence no vote will be meaningful. Egyptian democracy was stillborn.

Far from overcoming the divisions of the society where close to 25 percent of the world’s Arabs live, the developments of the past two-and-a-half years have sharpened them. Egypt’s polarizing spiral, evident in Islamist attacks on Coptic Christian churches and the killing of at least two dozen police officers in Sinai, seems unstoppable.

For the United States and Europe, this amounts to a colossal strategic failure. Nothing — and certainly not the outcome in Afghanistan or Iraq — was more important than getting Egypt right. President Obama, who began his presidency with an attempt to build bridges to the Arab and Muslim world through a speech in Cairo, has seen his greatest failure in that very city. Post-Tahrir Egypt stands now as a monument to America’s declining influence in the world, even in a nation receiving $1.5 billion in annual aid.

All that American money translated into no ability to restrain a largely American-trained military (including General Sisi). It translated into little ability to persuade Morsi to reach out beyond the Brotherhood and refrain from railroading through a divisive constitution.

The Obama administration has appeared hesitant and wavering, zigzagging from support for Morsi to acceptance of his ouster. The critical moment came before the July 3 coup (“a violent or illegal change in government” according to the Oxford English Dictionary). A military intervention was almost certain to end badly. It was a terrible precedent. But Secretary of State John Kerry offered the view that the army was “restoring democracy.”Just as bad, Obama said this: “While Mohamed Morsi was elected president in a democratic election, his government was not inclusive and did not respect the views of all Egyptians.” Those are dangerous words from an American president. They seem to relegate the importance of a free and fair vote.

What now? A knee-jerk reaction would be to cut off U.S. military aid. That, however, would only increase the possibility of internal and regional mayhem. It is tempting, given the Egyptian military’s unconscionable attack on its own citizens, but should be resisted. The real lesson in Egypt is of America’s dwindling power under a wavering president whose hesitancy reflects that of most Americans after a decade of interventions. The price Egypt will pay has only just begun to be reckoned.