When I talk to boys and young men at school and university about why they don’t call themselves feminists, the answer is never “because I hate women”. Instead, they tend to express reservations about “female supremacy” or “man-hating”. There’s still a lot of confusion about the word.

This week, HeForShe, the United Nations campaign aimed at engaging men in the battle for gender equality, kicks off its #GetFree tour, visiting universities and talking to students about the issue. So I spoke to a group of young male feminists to ask them how big a battle it will be to bring their peers into the feminist fold, and how difficult it is for young men to speak out about sexism in 2015.

A 23-year-old research student, who wanted to remain anonymous, told me: “I think most young men would not identify as feminists, either because they don’t like the word, or just [because of] a more general lack of knowledge of feminism, or fear that it amounts to a chip off their masculinity.”

Luke Bonnett, a 29-year-old engineering consultant, says: “It’s not something that young men talk about, at least not among my circle of friends. Often, when someone knows better but is still sexist, it’s difficult to convince them why what they’re doing isn’t acceptable and it’s not just ‘political correctness gone mad’.”

Sam Harman, a second-year student at Oxford University, adds: “I think perhaps the crucial factor for young men in these kinds of situations is how they think the room will react. If they’re likely to get a good reaction, they’ll tend to speak out. If they think they will come across as a nit-picker or a ‘sissy’, it’s far rarer.”

Stephen Burrell, 27, is a PhD student at Durham University researching domestic violence prevention work with young men. He agrees that anxiety about masculinity is a key issue. “There’s a huge amount of pressure among your peers – especially in environments such as school or university – to behave in certain, ‘masculine’ ways, which frequently involve highly sexist and misogynistic behaviour.”

But Ethan Vince-Urwin, 20, a student at the University of York, says: “I think an increasing number of young men are beginning to feel very strongly about the issue and are standing up and being counted. I used to feel like feminism was something that only women could be part of, but it now portrays itself as a much more inclusive movement.”

On my visits to schools and universities, it has been clear that behaviours such as sexual harassment, rape jokes and sexist abuse are the preserve of a very small but vocal minority of young men. Most of my interviewees agree that those identifying as feminists – outwardly, at least – are also probably in the minority. So what about the critical mass of guys in between? Could engaging them be the key to swaying the balance?

Burrell says: “To refuse to go along with sexism and to speak out against it amidst such pressure can be really difficult – I know because I have often failed to do it myself. But as soon as one guy does it, they might be surprised about just how many of their peers agree with them, and how many were also too scared to say something.”

They say it also helps if discussions include the aspects of gender inequality and stereotypes that most directly affect boys. Hugh Taylor, 27, is a volunteer with Great Men, a project from the gender equality charity The GREAT Initiative, which runs workshops in schools with boys and young men aged 12-18. He says: “It’s important to note that things we might traditionally view as feminism or sexism make up only a small part of what we talk about. The main objective is to give them a platform to discuss issues that can arise from gender in general, and to try instil a sense of healthy masculinity. From this the discussion often leans towards issues such as homophobia or depression in young men and male suicide rates.

“From the boys in the workshops, misunderstanding is pretty common, but open hostility less so,” he says. “I’ve always been pleasantly surprised just how many young people actually seem to have a good grip on these issues. All that’s been missing is the chance to vocalise their opinions.”

The young men I interview all feel that the problem is a lack of understanding about feminism, rather than widespread antipathy towards it. Refreshingly, instead of calling for feminism to be “rebranded”, most of them point to education and male role models as the key to changing attitudes.

Callum Lynch, a 24-year-old student, says: “I think men should be unashamedly open about identifying as a feminist to help to remove the unwarranted stigma surrounding the term.”

Mark Woodward, head of careers at Bablake School in Coventry, has supported the creation of a school feminist society, but says he and one boy are currently the only male attendees. He told me: “I suspect the majority who stay silent in a group are afraid of standing out and being ridiculed. Teachers instigating [discussion] and making it OK to stand up have to be there as role models – that’s key.”

Jack Fletcher, 25, is the national coordinator for Sexpression:UK, a student organisation that runs sex and relationship sessions within the community. He notes that primary school children seem much more willing to discuss the problem of sexist behaviour than those in older age groups, “where other influences such as media and film may be playing a part in their views on life”. He says: “If comprehensive sex and relationship education was made a compulsory part of education, then the issues of gender inequality could be addressed.”

There is a general consensus that alongside more men speaking out more vocally, education is vital.

As Burrell puts it: “Young men are not inherently sexist or misogynistic. Those things are taught by the society in which we live, and they can also be unlearnt.”