Twitter's public apology to women who have been subjected to online abuse is another significant victory for those campaigning against online misogyny. It follows in the wake of the successful #FBrape campaign that persuaded advertisers to suspend their marketing activities on Facebook until it made a commitment to tackle "gender-based hate".

If men who threaten women with rape are held accountable for their crimes, and Twitter takes action to make its community safer for women, then it sounds as if life online is about to get better for everyone who isn't a misogynistic rape apologist. So why are some people unhappy about the progress of such campaigns?

First, there are those who are rightly concerned about how we navigate a sensible pathway between free speech and hate speech. As Professor Susan Benesch, founder of the Dangerous Speech project in New York, said recently: "Facebook, Google and Twitter have more power to regulate speech worldwide than anyone else (including governments) has ever had. This is enormous power that should be used with great care."

If social media simply reflect social problems such as misogyny, there is a danger that making spaces such as Twitter and Facebook more censorious could simply limit everyone's free speech without properly understanding or tackling the wider problem of hate speech.

Second, there is the issue of how we tackle violence and abuse full stop. Anyone following the debate about gender hate-speech on social media in recent months could be forgiven for thinking that online abuse is always perpetrated by men and suffered by women. And yet a survey by the website Knowthenet in 2011 found that 19-year-old males were most at risk from cyberbullying among teenagers, with 85% saying they had been victims, while figures from the World Health Organisation reveal that men account for 81% of violent deaths globally every year.

In reality, men and women of all backgrounds are vulnerable to online abuse and it can come from the unlikeliest of places. Last week, the men's lifestyle magazine GQ published some of the violent threats tweeted at them by One Direction fans for making singer Harry Styles apparently look like a "man whore" in a recent cover shoot. Much like the offensive tweets directed at feminist campaigners, the online abuse of GQ's staff included death threats and threats of sexual violence, with calls for all the men who work for the magazine to be castrated.

Where is the outcry when One Direction fans threaten to mutilate the genitals of male journalists? Why is a Facebook group called "If Girls Get Period Pains Why Don't Boys Get A Kick In The Balls Once A Month" deemed acceptable? And why are so many women tweeting with the hashtag #KillAllMen?

This week, the Sky News journalist Niall Paterson spoke out for the first time about the emotional impact he suffered when a female tweeter sparked a barrage of online abuse after he broke the story that Gordon Brown was recorded calling a woman a bigot during the 2010 election campaign.

If you cast a wide enough net you soon discover that online abuse is not limited by gender. If we want to live in a less sexist society it does mean finding ways to tackle misogyny. It also means taking time to understand and address the experience of male victims of violence and abuse too.