Last Friday afternoon, the president of the Chicago Teachers Union, Karen Lewis, was speaking before an audience of thousands. It was the headliner rally of Chicago’s “day of action,” a massive citywide protest that brought together a disparate coalition of organizations: most prominently the teachers union but also the Fight for $15 group of low-wage workers, transit workers, nurses, South Side community groups involved in the fight for a trauma center in Hyde Park, pro-Palestinian activists with “Free Rasmea Odeh” signs, and multiple offshoots of the Black Lives Matter movement. All had come together in a remarkable European-style “general strike” to protest the austerity policies of Chicago Mayor Rahm Emanuel and Illinois Gov. Bruce Rauner.

While Lewis, who is black, was speaking, a group of young black attendees at the front of the crowd started chanting “Get cops out of schools!” loud enough for her to hear, according to several rally attendees. Lewis paused and told the chanters, “I tell you what—the cops are not our enemies. … If they let us, we will make them more helpful. Our kids are not criminals.”

If Lewis, who appeared to be speaking extemporaneously (though she has since repeated the sentiment on Twitter), didn’t think she was sharing a controversial notion, she was about to be schooled.

Immediately after Lewis, Page May of Assata’s Daughters, a grassroots collective of black female organizers that’s part of the Black Lives Matter movement, took to the podium with a different message. After a rousing speech about Black Lives Matter being “an affirmation for all people and a dream for the world,” May—who is a teacher, but at a private school, with no affiliation with the CTU—closed out with a nod to N.W.A.: “The last thing I want to say while I have all y’all’s attention is fuck the police, fuck CPD, fuck the FOP [Fraternal Order of Police]. … Fuck the police and everybody fuck with them.”

The reaction to May’s speech has been, shall we say, dramatic.

Since a local pro-police group posted the speech on its Facebook page on Monday—the caption read, “If there is a clear case of corruption and injustices in our governmental systems … look no further then the CTU and their many hidden agendas”—May’s speech has been viewed nearly half a million times. “This educator does NOT speak for any of the teachers in Chicago,” the post said. “She speaks for her own agenda….and she now teaches our children to HATE.”

While some Facebook commenters noted the disjunction of May’s role as a radical speaker and a molder of young minds, far more resorted to sick-making, racist, sexist personal attacks. Anonymous commenters on a police blog also contributed epithets and insults, along with details of May’s upbringing, sexuality, and the address of the school where she teaches. (One commenter: “FOP should rent a Billboard truck with her picture pasted on the side with audio and park it in front of her school and play audio when the students and parents are there in the morning and again in the afternoon at dismissal.”)

The Chicago FOP is now demanding that the CTU condemn May’s remarks; so far, the union’s only response has been to say that May isn’t a union member and that it had no prior knowledge of her speech. Still, the sequencing of the speakers, which was put together by the same coalition of organizations behind the day of action, has created some PR difficulties for the CTU, including within its own ranks. (The union has not responded to multiple requests for comment.)

Only in Chicago, it seems, would a teachers union—a reliably liberal but generally establishment institution in most American cities—land in such a quagmire. In 2010, a group of union members called the Caucus of Rank-and-File Educators, or CORE, won the leadership of CTU. Since then, CTU, which is the third-largest local teachers union in the country, has taken more aggressive steps to support its black and brown student population, which constitutes 85 percent of the CPS student body. In October 2014, the CTU sent buses to Ferguson, Missouri, to protest the killing of Michael Brown by a police officer, and last November, the CTU joined Black Lives Matter—specifically, Black Youth Project 100 (or BYP100), a group focused on ending police brutality, or abolishing the police altogether—in the Black Friday protests following the release of the video showing Laquan McDonald being shot 16 times in the back.

Endorsing the Black Friday protests was an unconventional and potentially risky move for the union, whose members’ politics tend to be far more centrist than BYP100’s and other groups that fall under the Movement for Black Lives umbrella. But since a successful 2012 CTU strike “really energized the left in this city,” according to one local leader, the union’s leadership has gone openly head to head with Emanuel, repeatedly calling for his resignation, and has become more involved with social justice issues that go beyond the classroom. Such a move is in keeping with our political times, and a consequence of many Chicagoans’ growing dissatisfaction with their city’s municipal institutions. But for many Chicago teachers, that hasn’t made the shift any less awkward.

Johnaé Strong is a CTU member—formerly a classroom teacher, now a restorative-justice coordinator at a CPS high school—as well as a Black Lives Matter activist, a member of both BYP100 and Assata’s Daughters who co-wrote a powerful Nation piece last month that directly connects police brutality to the underfunding of Chicago schools. “CTU is in a transition period,” she told me. “Its members understand that this is an important political moment and as a union we’ve taken some very explicit, forward-facing steps in messaging. But, of course, there are 27,000 people in the union and not everyone is a supporter, so there’s some tension there.”

And it’s true there are plenty of union members who seem to agree that the CTU should forcefully denounce May’s speech. (Notably, while only 9.4 percent of CPS students are white, 36.4 of its staffers are.) The sentiments of this anonymous commenter sums up a lot of the anger being directed toward CTU in the wake of this dust-up: “Our union president needs to step down NOW. She is no longer our leader and, hopefully, the teachers of Chicago will smarten up … when we need to choose a new leader. We love our policemen and firemen.” On Thursday, the union’s governing body voted to cancel an upcoming election in which Lewis and the rest of the CORE slate were running unopposed.

And even a radical-leaning union is still a union, says Mariame Kaba, the director of Project NIA, which has been a leader in bringing restorative-justice practices to Chicago schools. “They have to toe the line around their fellow union people,” Kaba said. “They’re not going to come out and say we don’t need police in schools.”

So what happens now? Will this messaging mess distract the CTU from other urgent (and not-unrelated) crises plaguing Chicago schools, like the huge midyear budget slashes still being announced, which already disproportionately hurt the poorest communities? In a time of constant staff cuts and furloughs, can the CTU use this opportunity to sell its moderate members on a more radical agenda?

For her own part, May isn’t backing down in the face of harassment that has included death threats: “I knew my speech would make a lot of people uncomfortable and angry, and I’m fine with that; if you’re not uncomfortable and angry, then you’re not seeing the problem.”

May even sees a bright side to all the outrage she’s provoked. “What’s really exciting to me is that teachers are talking,” she said. “They’re saying, ‘What did you think about what she said?’ There’s now dialogue happening among regular teachers who maybe hadn’t been talking about what it means to support the police, what it means to end the school-to-prison pipeline, and I think that’s important. We need those conversations. I’m fine being the person who showed up and was intense and said like, ‘Yo, you have to make clear which side you are on.’ ”

But with a membership roster encompassing tens of thousands of very different people, taking sides, as the CTU is learning yet again, is by no means a simple task.