IT shows how gifted Jon Stewart is that his best moment happened on someone else’s show. He appeared in 2004 on “Crossfire,” a CNN yelling program, and asked the hosts to take seriously their responsibility to public understanding by having useful conversations instead of shouting matches.

It was Mr. Stewart’s finest hour. He made an earnest pitch for civility in a place where there really was none. Which makes it too bad that in his 16 years of hosting “The Daily Show,” he never lived up to his own responsibility. His prodigious talents — he was smart and funny, and even more of both when he was mad — perfectly positioned him to purge a particular smugness from our discourse. Instead, he embodied it. I loved watching him, and hated it too.

Many liberals, but not conservatives, believe there is an important asymmetry in American politics. These liberals believe that people on opposite sides of the ideological spectrum are fundamentally different. Specifically, they believe that liberals are much more open to change than conservatives, more tolerant of differences, more motivated by the public good and, maybe most of all, smarter and better informed.

The evidence for these beliefs is not good. Liberals turn out to be just as prone to their own forms of intolerance, ignorance and bias. But the beliefs are comforting to many. They give their bearers a sense of intellectual and even moral superiority. And they affect behavior. They inform the condescension and self-righteousness with which liberals often treat conservatives. They explain why many liberals have greeted Tea Partiers and other grass-roots conservatives with outsize alarm. They explain why liberals fixate on figures such as Sarah Palin and Todd Akin, who represent the worst that many liberals are prepared to see in conservatives. These liberals often end up sounding like Jon Lovitz, on “Saturday Night Live,” impersonating Michael Dukakis in 1988, gesturing toward the Republican and saying “I can’t believe I’m losing to this guy!” This sense of superiority is hardly the only cause of our polarized public discourse, but it sure doesn’t help.

And Mr. Stewart, who signed off from “The Daily Show” on Thursday,was more qualified than anybody to puncture this particular pretension. He trained his liberal-leaning audience to mock hypocrisy, incoherence and stupidity, and could have nudged them to see the planks in their own eyes, too. Instead, he cultivated their intellectual smugness by personifying it.

I don’t mean the know-it-all persona he adopted on the air. That’s normal for a host. If anything, he was unusually self-deprecating for his line of work. And I don’t mean that Mr. Stewart thought all progressives were perfect. When some self-styled smart liberals didn’t vaccinate their children, he cracked: “They’re not ignorant. They practice a mindful stupidity.” But there was no doubt where he tilted politically. Conservatives were his main target when George W. Bush was president, and also when Barack Obama took office.

His claims to be objective fell flat. For instance, Mr. Stewart denied being in President Obama’s corner by re-airing a clip in which he had made fun of the Obamacare website’s rollout, as if that was the same as questioning Obamacare itself. That was par for Mr. Stewart’s course, mocking liberals’ tactics and implementation but not their underlying assumptions or ideas.

He could have made the liberals in his audience more open to dialogue across the great left/right divide by asking them to examine themselves more carefully and to admit that both ideological camps contain fools. Instead, he was a cultural entrepreneur who provided those viewers with the validation they wanted.

Maybe that’s why my strongest memory of Mr. Stewart, like that of many other conservatives, is probably going to be his 2010 interview with the Berkeley law professor John Yoo. Mr. Yoo had served in Mr. Bush’s Justice Department and had drafted memos laying out what techniques could and couldn’t be used to interrogate Al Qaeda detainees. Mr. Stewart seemed to go into the interview expecting a menacing Clint Eastwood type, who was fully prepared to zap the genitals of some terrorist if that’s what it took to protect America’s women and children.

Mr. Stewart was caught unaware by the quiet, reasonable Mr. Yoo, who explained that he had been asked to determine what legally constituted torture so the government could safely stay on this side of the line. The issue, in other words, wasn’t whether torture was justified but what constituted it and what didn’t. Ask yourself how intellectually curious Mr. Stewart really could be, not to know that this is what Bush administration officials had been saying all along?

Mr. Stewart later acknowledged that Mr. Yoo had bested him, which didn’t happen very often. In that sense, the interview was an outlier. But it wasn’t a coincidence. Mr. Stewart had gone in lazy, relying on a caricature, and seemingly unprepared for the thoughtful conservative sitting in his guest chair.
After all those years, the comedian turned liberal standard-bearer still didn’t really comprehend the conservatives on the other side of the divide. 

Worse, he didn’t help his liberal viewers better understand themselves.

Correction: August 7, 2015
An earlier version of this article included the incorrect name of the “Saturday Night Live” cast member who impersonated Michael Dukakis in a 1988 sketch. It was Jon Lovitz, not Dana Carvey.
GERARD ALEXANDER is an associate professor of politics at the University of Virginia.