The Department for Education's statutory guidance on relationships, sex and health education already says schools should "be alive to issues such as everyday sexism, misogyny, homophobia and gender stereotypes and take positive action to build a culture where these are not tolerated".
It says secondary pupils should be taught about consent, the negative impacts of pornography on sexual relationships, and that sharing and viewing of indecent images of children is a crime.
Updated guidance, published this summer and due to be rolled out from September, specifies that pupils "should be equipped to recognise misogyny" as well as its links to violence against women and girls, and understand the importance of challenging it.
Paul Whiteman, general secretary of school leaders' union NAHT, said it was positive the government was recognising the importance of training and support for school staff but said schools were "just part of the solution".
Pepe Di'Iasio, general secretary of the Association of School and College Leaders, welcomed the government's focus, but added it was essential that the government introduced "effective measures to prevent at source the spread of online misogynistic content which is served up to young people by social media algorithms".
Conservative leader Kemi Badenoch suggested the classes for teenage boys were only being rolled out because "some people in Labour" watched Adolescence - the Netflix drama that explored the impact of social media and influencers on teenage boys.
She said £20m was "a pittance" and the government needed to put more police officers on the street, stop "people, who come from cultures that don't respect women, coming into our country", and remove foreign criminals as soon as they commit crimes.
Liberal Democrats spokeswoman for women and equalities Marie Goldman welcomed training for teachers but said unless it was accompanied by steps to "properly moderate online content" she had no doubt it would fail.