“Every power to exert symbolic violence, i.e. every power which manages to impose meanings and to impose them as legitimate by concealing the power relations which are the basis of its force, adds its own specifically symbolic force to the power relations.”
Reproduction in Education, Culture, and Society was first published in 1970. In their Afterword to the 1990 edition the authors note that the most misunderstood idea in the book was "symbolic violence." They were misunderstood to be saying that some teaching - the teaching that reproduced the domination of the dominant class - imposed a culturally arbitrary content with a false authority, an authority that ultimately rested on force. Bourdieu and Passeron clarified that they were asserting the more radical proposition that all teaching imposes a culturally arbitrary content with a false authority, whether it be from the dominant class or from any attempt to subvert the dominant class.
The reason they call this "violence" is to draw a parallel between the school and the state (which are, of course, often the same institution). Max Weber said that the state is the institution with a monopoly of legitimate physical violence. The school, Bourdieu and Passeron argue, is the institution with the monopoly of legitimate symbolic violence. Each uses its authority to assert the dominant culture and to suppress threats to that dominant culture.
I quarrel with Bourdieu and Passeron for calling this action of teaching "violence." The term is almost always inappropriate and unnecessarily provocative.
My larger quarrel with them, though, is over the idea that all of the content of teaching is a cultural arbitrary imposed to bolster the social position of the teaching class and those they represent. The authors are making a large metaphysical claim that there are no fundamental truths that transcend class position.
I accept just about every claim of epistemological modesty that it is extraordinarily difficult to know with certainty what it fundamentally true. I contend as a claim of faith that there are some truths, though. I am happy to have my contentions compete with other faiths in the marketplace of ideas. Bourdieu and Passeron also allow what they call the "reality principle" or "law of the market": if the market validates a kind of teaching, it has more authority. But they do not grant that this authority reflects on the truth of the claim - only that it helps people believe it is true. Yet they also think that it is hopeless to try to teach with authority that all truth is relative.
I don't think Bourdieu and Passeron's claim about the truth of their own claims about truth are coherent.