Berkeley, California (CNN) Judging from the talk about the University of California, Berkeley lately, you'd think the campus was filled with hypersensitive snowflakes covering their ears to block out ideas they don't like.

The school's latest free-speech controversy came this week when student groups bailed on a planned Thursday speech by right-wing commentator Ann Coulter, who later called the campus of 40,000 students a "radical thuggish institution."

It's true that in recent months, protests on or near this bucolic campus have turned violent. Earlier this month, 21 people were arrested when opposing groups clashed in a city park over President Donald Trump's policies, and in February an appearance by right-wing provocateur Milo Yiannopoulos was canceled amid near-riots.

But walk around Cal Berkeley for a day and you won't find thugs. Many students will tell you they support Coulter's right to speak, even if they disagree with her. The university should have found a way to make it happen, they'll say.

A few will also tell you that the traditionally liberal campus -- which saw two peaceful protests Thursday -- needs to be more open to hearing opinions that don't emanate from the left.

UC Berkeley student Harmanjit Sodhi, 20, a junior studying molecular and cellular biology: "I think if you don't support the popular left opinion -- even if you're a moderate -- people are not willing to listen."

'These are ideas, but...'

Sitting under the 300-foot-high Campanile clock tower enjoying a sandwich, Harmanjit Sodhi, 20, told CNN that she was liberal growing up in Tracy, California. But Berkeley's leftism pushed her to the center.

Many of her classmates are quick to label someone a bigot or "sh**ty person" if they divert even slightly from core left-wing values, she said.

JUST WATCHED Coulter: Why can't we question liberals' patriotism? Replay More Videos ... MUST WATCH Coulter: Why can't we question liberals' patriotism? 02:59

"I don't like the fact (Coulter's speech) was canceled because at the end of the day, just because she's a Republican or has views most students disagree with doesn't mean her views aren't valid," said the junior studying molecular and cellular biology.

At the same time, Sodhi, like many students and faculty, feels Coulter's speech was a publicity stunt, aimed at painting the nation's cradle of free speech as intolerant.

School officials said the Berkeley College Republicans and Young America's Foundation, who had planned to host Coulter, didn't follow procedure. Citing violence during recent speaking events and protests , the school also said it was concerned about security.

These were the flyers put up around campus ahead of Ann Coulter's speech at #Berkeley. pic.twitter.com/mbU324BCv0 — Eliott C. McLaughlin (@EliottCNN) April 27, 2017

Now both groups are suing the university , and several provocative right-wing speakers -- including Yiannopoulos and white nationalist Richard Spencer -- have vowed to deliver remarks on campus later this year.

"Everybody's speaking, and nobody's listening," said junior Guutaa Regassa as he worked on his laptop in Sproul Plaza, the site of many free-speech battles in the 1960s. "These are ideas, but we're also human beings. I think people attack the human being when they need to attack the idea."

Berkeley a symbol

UC Berkeley graduate student Jacob Slater-Chin, 24, reads an "anti-fascist" flyer denouncing Coulter's planned visit to campus. He says he's bothered she won't be speaking.

They don't call it "Bezerkeley" without reason. Students have gotten rowdy here for decades, and the school's history of protest and political activity has sparked tangible change across the nation -- especially in the realm of free speech.

"When something related to free speech happens here, it gets the attention of the national press," said Robert Price, the associate vice chancellor for research, who has been teaching at Berkeley since 1970.

As for the recent violence, Price and several Berkeley students believe that students were only minimally involved in the melees. They suspect hate groups and Bay Area anti-fascists used these events to wage violence against each other.

"Obviously, they did that because Berkeley's a symbol," Price said.

But the political science professor is disturbed by what he feels is an aversion to the free exchange of ideas, which flouts the victories for which so many in the free speech movement of the 1960s fought and sacrificed.

In #Berkeley's Sproul Plaza, epicenter of the Free Speech Movement in the 1960s, a marker says, "This soil and the air space extending above it shall not be a part of any nation and shall not be subject to any entity's jurisdiction." A post shared by Eliott C. McLaughlin (@eliottmc) on Apr 27, 2017 at 5:54am PDT

Students back then appreciated that universities were supposed to make them uncomfortable, he said. They engaged in heated debates in Sproul Plaza. Price called it a "feast of intellectual combat," and no topic was off limits. Even Communists could be found in the plaza arguing among themselves -- Maoism versus Stalinism and so on.

Knowing this history firsthand, Price finds it disturbing that some students today want safe spaces and trigger warnings to fend off speech they find objectionable.

"To say it violates the First Amendment is true, but the threat is larger than that. If (students) believe something strongly, that belief ought to be embedded in something they can defend intellectually, and you only get that if you're challenged," he said.

"If you're so psychologically weak that the expression of ideas is going to traumatize you, you shouldn't be at a university."

A little history

Price remembers being a graduate student in October 1964 when police converged on Sproul Plaza to arrest Jack Weinberg for violating the school's ban on political activity on campus.

Berkeley students had been heavily engaged in the civil rights movement that year, both in the South and locally, and Weinberg was a leader with the Congress on Racial Equality . Local leaders had frowned on the demonstrations and pressured UC Berkeley to end it, Price said.

Cal-Berkeley Professor Robert Price recalls being in Sproul Plaza in October 1964, when Free Speech Movement leader Jack Weinberg was arrested and students surrounded the police car, preventing it from leaving for 32 hours. A post shared by Eliott C. McLaughlin (@eliottmc) on Apr 26, 2017 at 4:15pm PDT

When police cuffed Weinberg and placed him in the back of a squad car, a few students blocked the car's path , preventing it from leaving. Soon, there were dozens of students, then hundreds, then thousands.

Some, including Weinberg, actually mounted the police car's roof to deliver statements on free speech. The students remained in the plaza for 32 hours, until charges were dropped and Weinberg was released.

Demonstrations and rallies followed. Hundreds were arrested during a sit-in. Singer Joan Baez performed on the steps of Sproul Hall. By December of that year, the university approved eight resolutions lifting limitations on free speech , a phenomenon that quickly spread around the country.

Mario Savio, right, speaks at a "Peoples Park" free-speech rally at UC Berkeley in June 1969.

In a phone interview, Weinberg told CNN he felt the university was "ham-fisted" about the Coulter speech. He doesn't agree with Coulter, but he also doesn't agree with those who would retreat to safe spaces to avoid her message, nor with bullies "with no principles of their own" who would use her speech as an opportunity to engage in violence.

"My hope is she does not get prevented from speaking, and my hope is that thousands of people come out, just like during the free speech movement, and protest her message," he said Wednesday.

UC Berkeley student Guutaa Regassa, 21, a junior studying sociology and environment. He says it's been a "dark time" on campus since the November election and students seem to be arguing more.

'They're kind of, ironically, being Nazis'

Luise Valentin, a senior from Copenhagen, Denmark, said the university is certainly not above debate. While she cheekily says UC Berkeley students "are very much for diversity and free speech as long as you agree with us," she says the recent violence is anything but typical.

She has a class with public policy professor Robert Reich, a Democrat and political commentator who served in the Jimmy Carter and Bill Clinton administrations. After the most recent violence at Berkeley, Valentin said, Reich canceled his lecture for the day and instead engaged in a debate with former GOP Sen. Alan Simpson of Wyoming.

UC Berkeley student Ryan Kelley-Cahill, 19, a freshman studying business and political science: "If you have certain ideas that aren't expressed, they just build up in their own little bubble."

The purpose was "to show you could be open-minded and friendly with each other and still disagree," the 22-year-old said.

Many students say they aren't worried about classmates becoming violent if right-wing pundits deliver on promises to speak in Sproul Plaza. Ryan Kelley-Cahill, 19, a freshman from nearby Alameda, said he sees students civilly debating there every day over animal rights, foreign oil, Palestine and myriad other issues.

"The culture on campus, it's not like there are violent people going around trying to suppress people's views," the business and political science major said.

But those fringe elements -- the anti-fascists, the neo-Nazis -- concern some students who told CNN they think school administrators were trying to protect the campus by rescheduling Coulter's speech.

Jacob Slater-Chin, 24, a graduate student in multimedia, feels otherwise. Conservative views aren't freely aired on campus, he said, adding that he was "kind of interested in what Ann had to say." He is particularly annoyed, he said, by the black-clad anti-fascists, who he couldn't differentiate from the hate groups fighting during the Yiannopoulos speech and Trump rally.

"They're kind of, ironically, being Nazis," he said. "It doesn't really help your argument when you're literally beating up people."