Much of the movement grew out of 2nd wave feminism - at the time, shit was happening when it came to violence against women, rape within marriage, etc. One such notable moment in the UK was the Yorkshire Ripper case. The police's response at the time was to effectively place a curfew on women by telling them to not go out in the evenings or go without their husbands. This started a reaction because if anything (and I agree considering the context of societal attitudes towards women at that time), why not place a curfew on men instead whilst they tried to capture the Yorkshire Ripper? Hmmm, sexism.
Women also found that even amongst some Left political circles, their voices were invariably drowned out by men. Women's spaces came about to empower women and desire to make them look politically at their position and roles in society and how that could be challenged. Primarily to make women's lives better, but actually that by breaking down gender that it could benefit men too.
There's DV campaigns and safe spaces for various parts of the LGBT community too, and the last 10 years has seen much better organisation and information for men affected by DV also. There's also a rising MRA movement but frankly they're usually a bunch of right-wing fruitloops who seem to want to preserve traditional gender power structures rather than breaking them.
I appreciate what some say about unified campaigning and organisation about violence (and there is some umbrella organisation), but it's important that different types of violence and abuse are understood and their causes analysed - whether it be institutional and societal sexism, homophobia, the power structures that exist been genders, classes, races, straight/cis and LGBT, etc. Safe spaces and marches support that environment - and I mean, FFS, most of these happen for less than a day on one day each year, and yet still some people still think it's some sort of direct attack on them.