Serious people are beginning to talk up the idea of an alliance between the US and Syrian dictator Bashar al-Assad against the seemingly unstoppable forces of the Islamic State (IS, also known as ISIL or ISIS).

Ryan Crocker, former US ambassador to both Baghdad and Damascus, and a man whose opinion I value, argues that Assad is “the least worst option” in Syria. Richard Haass, who heads the Council on Foreign Relations, and is a foreign-policy realist, has written an opinion piece in the Financial Times (paywall) suggesting such an alliance may be the only way to defeat the terrorist group. (Haass and I briefly debated the point on MSNBC’s Morning Joe.)

It makes for a fascinating thought experiment. The argument goes like this: US airstrikes against some IS targets in Iraq won’t defeat the terrorists; to defeat them, we must fight them in all their safe havens, including those in Syria; to do that, we’ll need boots on the ground as well as airstrikes; President Obama won’t send US troops into Syria (or anywhere else); the non-Islamist Syrian opposition isn’t much of a fighting force; the only force capable of fighting the IS on the ground is Assad’s military; therefore, we should partner with Assad.

The philosophical quandary such an alliance would present—we’d be supporting a tyrant who has killed tens of thousands of his own people—is waved away with an old precedent: the Western powers partnered with Josef Stalin, no slouch at slaughter, against Nazi Germany.

But beyond the parlor game of what-if, an alliance with Assad would be a terrible idea, even for those who are willing to set aside the obvious moral issue. If anything, such a partnership would make matters much, much worse.

Here are four reasons why:

1. Western support for a Shia dictator (Assad is an Alawite, a branch of Shi’ism) would be propaganda gold for IS. One of the group’s foundational grievances is that the US-led invasion of Iraq handed power in Baghdad to the Shia and cast the Sunnis—in IS’s view, the legitimate rulers of Mesopotamia—into the cold.

Were Obama to make a compact of convenience with Assad, it would play into that narrative: The West is taking sides in Islam’s internecine war. This would turbo-charge what is already a rallying cry for IS leader Abu Bakr al-Baghdadi, and bring even more Sunni radicals to his banner.

2. It would outrage many Sunni states—Saudi Arabia, Turkey, Kuwait, the United Arab Emirates, et al—that view the civil war in Syria as a sectarian conflict. To many in those countries IS is a threat, but Assad is the greater evil. Any hope that Sunni countries would join the fight against IS would be extinguished by a US-Assad alliance. Instead, some of these states would feel compelled to resume covert support for IS.

3. It would empower Hezbollah, the Lebanese Shia terrorist group that enjoys Assad’s backing. Hezbollah fighters have been at the forefront of the fight against IS in Syria, acting as Assad’s shock troops. Supporting Assad would in effect mean supporting one terrorist group that has killed Americans against another.

4. It would give Assad, who gave IS crucial help to flourish in the first place, incentive to keep the group going (or at least prevent its destruction), in order to preserve his alliance with the West. Meanwhile, any money and material assistance delivered to Damascus will be used to enrich Assad and his generals, or used to pursue agendas that have nothing to do with fighting the terrorists. That’s pretty much the story of Pakistan, where US funding for counterinsurgency operations is often diverted to the acquisition of conventional weapons in the arms race with India, while the Pakistani military conducts elaborate (and ultimately ineffectual) feints against terrorist groups.

The choices facing President Obama are difficult and delicate. The challenge posed by IS is a complicated one, and the response from the rest of the world will be complicated, as well. But an unholy alliance between the US and Assad cannot be part of that response.