They are not at all like cops. This is a very complex topic, but basically teachers are, using Gramsci's terminology, "organic intellectuals", and they reproduce the ideology belonging to a certain class. Teachers are dangerous to capitalism because IF they have class consciousness they can pass those ideas to their students; basically creating well informed, critical students with class consciousness should be the goal of any marxist teacher. As neoliberalism advances to the school sector (at least here in south america), teachers lose and more and more of their freedom to actually give classes with anti-hegemonic ideas: bureaucratic work that has nothing to do with teaching is introduced, and they are forced to follow curriculums and textbooks with a bunch of pro-capitalist crap in them, and with very little in the way of actual knowledge. There are also actual fascist thugs in Brazil called "escola sem partido" ("school without a party") who basically bully and threaten teachers so that their children's education can be as conservative as possible. Of course, under this context, and with the curriculum that they are increasingly forced to follow, they become "organic intellectuals" of the bourgeoisie, but it's not really the fault of the teachers, and it's only the teachers, by acquiring class consciousness and through organizing, who can push back against this. We also increasingly speak more and more of the "proletarization" of the teachers here, who increasingly become more like factory workers, alienated from their labor, and with lower and lower salaries. Teachers are also necessary in ways that cops are not, since their work is to evaluate the level of development of children and make them surpass them, which is something only they can do (Vygotsky's "level of proximal development"). The problem is that capitalism doesn't allow the teachers to actually do their jobs correctly. I guess in summary, cops are class traitors whose main function is to protect private property. Teachers are workers who only perpetuate capitalist ideology when they are literally forced to and fucked over by the capitalist education system. Teachers have some revolutionary potential because of their ability to make working class students recognize and think critically about their condition, cops have absolutely no revolutionary potential since they are just fascist bullies. Of course, this is the case in Latin America anyway, I don't know what teachers are like in burgerland.