There are hundreds of studies which show that domestic abuse is usually close to 50/50 (here is a link to 500, here is a link to 286, and you can find 1700 here).
Some studies find that women are more abusive; for example this US study which says that for nonreciprocal domestic violence, women are 70% of perpetrators. When it comes to dating violence, studies again show women as the majority of perpetrators. Studies have been coming out since the 1970s saying this.
Male victims of domestic abuse have a 47% chance to be threatened by police, 35% of being completely ignored, and a 21% chance of being arrested themselves. If a man calls the police about being abused, he's three times more likely to be arrested than a woman. Of abused men who called domestic violence hotlines, 64% were told that they “only helped women.” In 32% of the cases, the abused men were wrongfully referred to batterers’ programs. A little over a quarter of them were given a reference to a local program that helped. 16% said the people at the hot line dismissed or made fun of them. In 2015 the United States Government will give $222 million in grants to combat violence against women. No money is earmarked to benefit males despite men being the majority of victims for violent acts.
One of the problems regarding domestic abuse is that only 9 states in the USA have shelters which offer help to abused men. There’s a huge legal and social bias against men in this regard (sometimes obvious discrimination), something which is perpetuated by certain models of violence (such as the Duluth Model).
The website for the Duluth model actually says that men are conditioned by society to abuse women, and women who abuse men only do so as a form of self-defense. This is hilariously inaccurate, as proven by the hundreds of studies I've linked to above, but the Duluth model is incredibly popular anyway — it "has been adopted in more than 4,000 communities in all 50 states, and at least 26 countries." [x] Oddly enough, the Duluth model's website briefly mentions domestic abuse in LGBT relationships, but doesn't address the logical inconsistency they've just created — if domestic abuse is all male on female violence stemming from "male entitlement", then what's their explanation for abuse in lesbian relationships? They link to a site called the Northwest Network which vaguely addresses some important points, and contains a PDF which says crisis line workers "tended to rate same-sex abuse as less serious, less likely to recur, and less likely to get worse over time than opposite-sex abuse. They also believed that it was easier for victims in same-sex relationships to leave their partners." The people behind the Duluth model seem to ascribe to this viewpoint since they only deem cisgendered heterosexual women to be legitimate victims of abuse.
LGBT relationships do experience violence, although studies are a bit mixed. Some say there's a higher percentage of violence than heterosexual relationships, while other say LGBT relationships are happier than the average relationship. The US prison with the highest rate of inmate-on-inmate rape is a women's prison even though fewer than 10% of all prisoners are women.
It's estimated that almost a third of abuse (physical, sexual, emotional) victims in Ireland are male. Men are 40% of abuse victims in the UK according to a couple of studies.
It's been theorized that women are now the majority of perpetrators when it comes to domestic violence (something some studies find to be true) because society has never made a big deal out of it. While men throughout history have been blasted for beating women (often punished by whipping), women haven't. When was the last time you heard of an abuser being lynched or personally beaten by the judge? Even abused husbands were ridiculed and punished (and still are). If modern society held all genders equally accountable for abuse, rates of domestic violence would possibly diminish.
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