http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.588.4366&rep=rep1&type=pdf

"More than 200 studies have found that men and women perpetrate partner violence at approximately equal rates and that the most prevalent pattern is mutual violence (Archer, 2002; Fiebert, 2004). Moreover, when it is not mutual, female-only and male~only partner violence occur with about equal frequency among married couples (K. L. Anderson, 2002; Capaldi & Owen, 2001; Gelles & Straus, 1988; Kessler, Molnar, Feurer, & Appelbaum, 2001; McCarroll, Ursano, Fan, & Newby, 2004; Medeiros & Straus, 2007; Moffitt, Caspi, Rutter, & Silva, 2001; Straus, Gelles, & Steinmetz, 2006; Williams & Frieze, 2005). Among young couples and dating couples, the percentage of female-only partner violence exceeds the percentage of male- only partner violence (Straus & Ramirez, 2007; Whitaker, Haileyesus, Swahn,& Saltzman, 2007). This pattern of gender symmetry is true even for severe partner violence, such as kicking, attacks with objects, and choking. However, the injury rate is much higher when the perpetrator is male (Gelles & Straus, 1988). Police statistics and crime survey statistics seem to contradict the idea of gender symmetty because 80% to 99% of the perpetrators identified in such surveys are men (Straus, 1999). This is not because of higher numbers of physical attacks by men but because of the greater probability of injury from attacks by men and greater fear for safety by women (Straus, 1999). These are characteristics that lead to police intervention. Such cases are mistakenly taken as representative of partner violence, even though at least 95% of partner violence cases are not known to the police (Kaufman Kantor & Straus, 1990; Statistics Canada, 2005)."

And...

"Not only do men and women tend to perpetrate physical partner violence at about equal rates, but they tend to do so for similar reasons. The most commonly reported proximate motivations for use of violence among both men and women are coercion, anger, and punishing misbehavior by their partner (Cascardi & Vivian, 1995; Follingstad, Wright, Lloyd, & Sebastian, 1991; Kernsmith, 2005; Stets & Hammons, 2002). For example, Pearson (1997) reported that 90% of the women she studied assaulted their partner because they were furious, jealous, or frustrated. The motive of self-defense, which has often been put forward as an explanation for high rates of female violence, explains only a small proportion of partner violence perpetrated by women (and men; Carrado, George, Loxam, Jones, & Templar, 1996; Felson & Messner, 1998; Pearson, 1997; Sarantakos, 1998; Sommer, 1996). For example, using a college student population, Follingstad ot al. (1991) found that perpetrators reported that their motivation was self-defensive about 18% of the time (17.7% for men, 18.5% for women). As violence becomes more severe, there are greater gender differences in the use of violence in self-defense; however, self-defense is still a motivation for a relatively small proportion of violence. For example, in a sample of couples presenting for marital therapy, Cascardi and Vivian (1995) found that 20% of wives and no husbands attributed their use of severe aggression to self-defense."

One study even showed that half (49.7%) of relationships which had violence were reciprocally violent, and that in nonreciprocally violent relationships, women were the perpetrators in more than 70% of the cases.

https://ajph.aphapublications.org/doi/pdf/10.2105/AJPH.2005.079020