Two men I admire, U.S. Senator John McCain and Robert Kagan of the Brookings Institution, have recently argued that the U.S should suspend aid to Egypt after the army coup last week that ousted President Mohamed Mursi of the Muslim Brotherhood.

“We cannot repeat the same mistakes that we made at other times in our history by supporting the removal of freely elected governments,” McCain said. Kagan says that continuing aid to the Egyptian military will eventually be a source of embarrassment.

Given that the Egyptian army appears, at least according to initial reports, to have committed a massacre against Muslim Brotherhood members, the case McCain and Kagan made looks fairly strong. And it is no use arguing, as President Barack Obama’s administration seems to be, that what happened in Egypt last week wasn’t a military coup.

It was, even though it came with an asterisk: The coup might not have happened had millions Egyptians not taken to the streets to demand Mursi’s ouster. But to keep the aid flowing (as Noah Feldman explains here), the White House and Congress would need to find an exception to their own rules, which require suspending aid to countries when their leaders are deposed by military force. Finding a loophole could well be worth it: Cutting off aid might accelerate Egypt’s self-destruction, and harm American interests in the Middle East. Here are four reasons why:

1. Before this coup, there was another coup — and I’m not referring to the events that brought about the downfall of the Egyptian dictator Hosni Mubarak in 2011. In November, Mursi initiated an internal coup, placing himself, by decree, above the law to make sure that his Islamist constitution would be approved.

It was at this moment that the Obama administration should have considered suspending aid. As we now know, the White House didn’t consider doing very much at all. It maintained its close relations with Mursi, and mostly ignored the intense anger his actions sparked among Egyptians, anger that eventually exploded last week in mass demonstrations against his rule.

If the U.S. cuts aid now when it refused to do so after Mursi’s grab for absolute power, it will permanently alienate the millions of Egyptians who believed, with good reason, that Mursi was attempting to turn himself into an Islamist Mubarak. And these Egyptians — the ones who demonstrated against Mursi last week — are precisely the sort of liberals (or, at least, anti-fundamentalists) the U.S. should be cultivating.

2. Egypt’s military is preventing the Sinai Peninsula from becoming a haven for al-Qaeda and similar groups. If terrorists take over stretches of Sinai, they will launch attacks on Israel. Israel will respond by invading Sinai (again). This is not something the U.S. wants. What the U.S. wants is to maintain leverage over the Egyptian military in order to encourage it, and equip it, to prevent the spread of al-Qaeda-like extremism. Chaos in Sinai is not only a threat to Israel, but also to Jordan and the U.S. Chaos in the streets of Cairo and Alexandria isn’t in the best interests of the U.S. either, and that appears to have been where Egypt was heading last week.

3. In Pakistan, we saw what can happen when American military aid is cut off. After Pakistan went nuclear, the U.S. retaliated by punishing its army. Most notably, the U.S. stopped bringing members of the Pakistani officer corps to America for training. The result: a Pakistani officer corps that doesn’t know, or like, the U.S. And, of course, our boycott of Pakistan’s military didn’t actually end the country’s nuclear program. Cutting off the Egyptian military would only free it to behave more brutally toward its internal foes than it does now.

4. At this moment, it may be difficult for some people to focus on the venality of the Muslim Brotherhood. But let me help. In addition to being anti-democratic — it is the model of an extremist group that attempts to leverage the democratic process in order to subvert it — it is also a highly misogynistic movement, an anti-Christian movement and an anti-Semitic movement. Its worldview is antithetical to that of the U.S. The Obama administration and its ambassador in Cairo, Anne Patterson, made a mistake in coddling the Brotherhood over the past year. There’s no reason to continue that coddling now. Cutting off aid would, in effect, be signaling to the Egyptian people that the U.S. is on the side of the Brotherhood.

One other note: I try to resist the urge to judge people by their supporters, but I’ll make an exception here. Yusuf al-Qaradawi, the Sunni theologian and Al Jazeera commentator who serves as a kind of spiritual godfather to the Brotherhood, has called the removal of Mursi invalid and demanded his reinstatement. Qaradawi is a revanchist Muslim supremacist who has argued for female genital mutilation and for the physical punishment of gay men and lesbians. He has advocated suicide terrorism and argued that Hitler was carrying out God’s work when he murdered Jews.

Qaradawi’s vehement opposition to the Egyptian army’s ouster of Mursi makes me think that the millions of Egyptians who demanded his removal are on the right side of history.

Jeffrey Goldberg

Jeffrey Goldberg is a columnist for Bloomberg View, and a senior editor at The Atlantic.