First of all, this is a fight that Pelosi wanted.

"All these people have their public whatever and their Twitter world," Pelosi told Dowd. "But they didn't have any following. They're four people and that's how many votes they got."
That comment echoes what Pelosi said of AOC (and her closest allies, including Reps. Ilhan Omar of Minnesota, Rashida Tlaib of Michigan and Ayanna Pressley of Massachusetts) in an April interview with USA Today. "While there are people who have a large number of Twitter followers, what's important is that we have large numbers of votes on the floor of the House," Pelosi said.

Less than a week later, Pelosi was at it again. Asked by CBS' Lesley Stahl about AOC and her cadre, the speaker replied drolly: "That's like five people."

Three times Pelosi taunted them. Eventually Omar, Tliab, Pressley, and AOC were going to respond.
Why did Pelosi want this fight? Political hack Jonathan Chait gives a pretty good reason why.

What struck me is that AOC’s squad is doing her a huge favor by criticizing her from the left and turning her into a centrist. Pelosi used to be THE symbol of out-of-touch coastal liberalism. Now that symbol is AOC, and Pelosi is an Italian grandmother again.
...
The conservative media has done more than any other force to elevate the AOC squad. So, from Pelosi’s perspective, continuously pointing out that they’re four people is fighting back against conservative propaganda.

I hate to say it, but Chait is right about this...from a certain short-term perspective.
If all that matters is between now and November 2020, Pelosi is making a shrewd decision.
But from any other perspective, Pelosi is making a huge mistake.

Ben: All I’m saying is that mocking members of your own caucus comes off as churlish and seems like poor long-term strategy. There are plenty of ways to separate yourself from these members, and progressives writ large, without actively antagonizing them like this. It’s pretty easy to make the Twitter argument Eric mentioned without resorting to insults.

All of the energy in the Democratic Party is on the progressive side. The corporate establishment has to go to ever more extreme levels to keep progressives at bay, and young people are increasingly leftist.
So directly mocking this wing of the party is clearly stupid from a long-term view.

On Saturday, New York Times columnist Maureen Dowd published an interview with House Speaker Nancy Pelosi that reads like an excerpt from The Great Gatsby reimagined for the 21st century...Pelosi has had a rough go of it lately, and the Dowd interview is the strongest evidence yet that the most powerful Democrat in America is losing touch with the country.
...
When conservative Democrats backed by Gottheimer challenged Pelosi from the right after the November elections, the lefty freshmen stuck with Pelosi and urged their supporters to do the same. Pelosi has rewarded them with persistent contempt.

It's been obvious for many decades that the Democratic Party has nothing but open contempt for anyone and everyone on the left. Pelosi and Biden are aging Clinton-era Democrats that never saw any consequences for their betrayal of the working class, and thus never learned any lessons from it.
But like wealthy, comfortable liberals everywhere, they think they've got it all figured out because they don't realize that their basic assumptions are wrong.

"I don't think Alexandria and her friends ... they haven't learned, they haven't been in Congress enough to understand that negotiations happen in Congress," Aristimuño said. "They don't happen on Twitter, they don't happen on Facebook. She doesn't seem to understand that yet. Maybe later on she will understand it."
He then praised Speaker of the House Nancy Pelosi, a Democrat from California, saying he believed she's done a "tremendous job." Aristimuño explained that he thinks Pelosi is "trying to understand the left [of her party]." He argued that the speaker recognizes that she must work with Republicans to get stuff done.

Everyone knows that "working with Republicans to get stuff done" means "capitulating to their demands." Also, 'Pelosi is "trying to understand the left"' speaks volumes.
It's not just corruption when it comes to corporate Democrats. They honestly have no idea what is going on with the working class of this country. Nor are they all that interested in knowing. This feud is helping to expose this gaping flaw in Dem leadership.

Also, it's not just the four that Pelosi targeted.

When Pelosi, facing no help from Senate Democrats and a revolt from moderates within her own conference, “reluctantly” agreed to put on the floor the $4.6 billion Senate bill—which didn’t include improved standards for treatment in migrant detention facilities, and appropriated more enforcement money to the Defense Department—she exposed the underlying tensions within her caucus. The co-chair of the Progressive Caucus, Rep. Mark Pocan, asked on Twitter, “Since when did the Problem Solvers Caucus”—the group of moderates who demanded a vote on the Senate bill to get a bipartisan accomplishment under their belts before the July Fourth recess—“become the Child Abuse Caucus?” The tweet prompted two freshmen Problem Solvers, Rep. Max Rose and Rep. Dean Phillips, to confront Pocan on the House floor.

“Mark’s tweet just speaks to why everyone hates this place,” Rose told Politico. “He’s just trying to get retweets. That’s all he cares about.”

Yeh. It's not like anyone cares about child abuse.
This is being exposed because of the growing progressive insurgency in the Democratic Party. The more victories the insurgents gain, the more the Democratic leadership will be exposed for their out-of-touch elitism and corruption.
The insurgency is only one and a half election cycles old, and already it's become a problem for the Old Guard. Imagine what it might be like in 2021.