Last month, while visiting Egypt, I did a fascinating interview with a former Muslim Brotherhood leader named Mohammed Habib, who quit the group because its leaders had made dirty deals with Egyptian generals in the past.

At present, the Brothers and the generals are at loggerheads. The generals are trying to muddy the results of last weekend’s presidential runoff, in which the Brotherhood’s candidate, Mohammed Morsi, appeared to have beaten the military’s man, Ahmed Shafik. And last week, the military dismissed the elected parliament in which the Brotherhood controlled nearly half the seats.

But Habib’s words help explain the roots of the power struggle between the Brotherhood and the generals — a struggle that has hijacked the revolution. They also offer some clues about how U.S. officials should respond.

A grandfatherly, white-bearded geology professor, Habib was the senior deputy to the secretive organization’s supreme guide from 2004-09. We spoke in his comfortable living room in a brand-new, upscale apartment complex in a Cairo suburb.

Like many Brothers, Habib spent more than six years in prison at a time when the organization was banned under the regime of former president Hosni Mubarak. Yet, in a strange paradox, the Brotherhood had constant contacts with the Egyptian military and intelligence agencies.

“The regime’s strategy,” said Habib, “was to put the issue of the Ikwan (Brotherhood) in the hands of state security agencies.” The regime would alternately arrest members, then let them run for parliament while quashing secular opposition groups. That fed Mubarak’s narrative that democracy would lead to theocracy.

Regime strategy ensured a Brotherhood leadership that was secretive and authoritarian, subservient to a supreme guide, Mohammed Badie. “There was a loss of strategy or vision and an extreme concentration of power in the center,” Habib said.

When the revolution erupted, Badie’s response was to forbid the group to take part. (Around 2,500 young members defied him and went to Tahrir Square.) Even after Badie gave his members a green light to participate, he sent Morsi and another Brotherhood leader to meet secretly with the regime’s intelligence chief, Omar Suleiman.

“I begged them not to do it,” Habib said. “I said it would be a cause of shame to the organization, since Suleiman (wanted) to split the unity of the revolutionary forces.” But Badie authorized the meeting and ordered Brotherhood members to leave the square (young Brothers refused to go). That act impelled Habib to quit the organization.

Habib believes the candidates of the Brotherhood’s front party did well in parliamentary elections because Egyptians saw them as a clean face of the revolution. They could have built a broad political coalition and consolidated their popular support. Instead, they rode roughshod over other parliamentary blocs and broke their pledge not to run a candidate for president.

The military, which at first accepted the Brotherhood victory in parliament, came to see it as a threat, leading to the current confrontation. This puts U.S. officials — and Egypt’s pro-democracy forces — in a difficult bind.

No one wants a return to the old Egyptian order of corruption and repression, with Shafik replacing Mubarak (reports of whose death appear manipulated and premature.)

So members of Congress are already calling to cut off aid to Egypt’s military. But the Muslim Brotherhood has displayed a disdain for democracy that is equally disturbing, equating a parliamentary win with a license to control every institution. Its current call, under duress, to revive a coalition of democratic forces, is unconvincing.

Washington should make clear that Western aid (which Egypt desperately needs) will be contingent on respect for the rights of Egyptians from all parties, meaning SCAF and Brotherhood alike (or any others). In recent months, as Habib describes, the two have behaved like undemocratic twins.