In general (not domestic violence), and across cultures, men are more aggressive than women (Eagly and Steffen 1986).
In general (not domestic violence), direct, especially physical, aggression is more common in males and females at all ages, is consistent across cultures, and occurs from early childhood on, showing a peak between 20 and 30 years (Archer 2004).
Among female-perpetrated assaults in general (not domestic violence), men reported being victimized by females more than women and experiencing the more severe forms of assault more than women (George 1999).
In the United States, as elsewhere, men kill unrelated men about 40 times as often as women kill unrelated women (Daly and Wilson 1990).
In 2005, 21% of all homicides of partners in the United States were perpetrated by women (U.S. Department of Justice 2006).
Within western heterosexual partnerships, women are slightly more likely than men to use one or more act of physical aggression (Archer 2000).
Among non-Western nations, men are more likely to inflict violence on women than vice versa (Archer 2006).
In the west, women use acts of physical aggression to their heterosexual partners more frequently than men (Archer 2000).
The bias towards women being more aggressive than men in couples is stronger when the males are less agressive (Archer 2000).
The younger the couple, the more the female rate of assaulting a partner exceeds the rate for males. (Fiebert and Gonzalez 1997; Archer, 2000; Straus and Ramirez 2002).
Within western heterosexual partnerships, men are more likely to inflict an injury, 62% of those injured by a partner being women (Archer 2000).
In partner violence, physically violent men are far more deviant than physically violent women (Magdol, et al., 1997).
In partner violence, female victims suffer far more symptoms of anxiety than male victims (Magdol, et al., 1997).
According to the National Family Violence Survey, female victims of domestic violence are nine times more likely to call the police than male domestic violence victims (Stets and Straus 1989).
In domestic violence, women also commit more severe assaults than men (Straus 1999, 2004; Straus and Ramirez 2007).
Among heterosexual partners, women are more likely than men to throw something at the other, slap, kick, bite, or punch, and hit with an object. Men are more likely than women to beat up, and to choke or strangle. (Archer 2002)
Within couples, the woman is more likely to initiate violence (Demaris, 1992; Straus 1996).
Males appear to report their own victimization less than females do and to not view female violence against them as a crime (Dutton and Nicholls 2005).
When only one partner is violent, it is twice as likely to be the female partner as the male partner (Straus and Ramirez 2002).
The vast majority of stalkers are male and that the majority of victims are female (Douglas and Dutton 2001)
Stalkers tend to be in their mid-30s. Douglas and Dutton (2001)
Misleading research has tended to consistently err on the feminist side. Dutton and Corvo (2006)
Hypothesis
In r/K selection theory, r-selected species produce many offspring, each of which is unlikely to survive to adulthood, while K-selected species invest more heavily in fewer offspring, each of which has a better chance of surviving to adulthood. J. Philippe Rushton applies this theory to different human races.
Male-on-female domestic violence would be related to the likelihood of cuckoldry, which is higher in an r-selected race.
Female-on-male domestic violence would be related to the importance of resources provided by the male, which is higher in a K-selected race.
Summary
Men are naturally much more violent than women.
Men have far greater upper body strength.
Given the sex difference regarding what provokes jealousy one would expect greater male-on-female violence.
The above considered, when it comes to domestic violence in Western cultures, men are surprisingly restrained and women are surprisingly violent.
DEMARIS, A., 1992. Male versus female initiation of aggression: The case of courtship violence. In E. C. Viano (Ed.), Intimate violence: Interdisciplinary perspectives, pp. 111–120. Bristol, PA: Taylor & Francis.
STETS, J. E., and M. A. STRAUS, 1989. Gender differences in reporting marital violence and its medical and psychological consequences. In M.A. Straus & R.J. Gelles (Eds.), Physical Violence in American Families: Risk Factors and Adaptations to Violence in 8,145 Families (pp. 227-244). New Brunswick, NJ: Transaction Publishing.