This logic is flawed. Men do not commit more violence than women it is because the effects of violence are more impacting. Males are stronger therefore this results in increased injury.
Lesbian partner violence is a huge issue.
“The Centers for Disease Control and Prevention (CDC)’s 2010 National Intimate Partner and Sexual Violence Survey reports on the lifetime prevalence of rape, physical violence or stalking by an intimate partner, focusing for the first time on victimization by sexual orientation. It finds a victimization prevalence of 43.8 percent for lesbians, making it the second most affected group after bisexual women (61.1 percent), ahead of bisexual men (37.3 percent), heterosexual women (35 percent), heterosexual men (29 percent) and homosexual men (26 percent)”