You do know the definition of domestic violence that is used in compiling the stats don't you ?
"Any incident or pattern of incidents of controlling, coercive or threatening behaviour, violence or abuse between those aged 16 or over who are or have been intimate partners or family members regardless of gender or sexuality. This can encompass but is not limited to the following types of abuse:
- psychological
- physical
- sexual
- financial
- emotional
Controlling behaviour is: a range of acts designed to make a person subordinate and/or dependent by isolating them from sources of support, exploiting their resources and capacities for personal gain, depriving them of the means needed for independence, resistance and escape and regulating their everyday behaviour.
Coercive behaviour is: an act or a pattern of acts of assault, threats, humiliation and intimidation or other abuse that is used to harm, punish, or frighten their victim.” *"
So domestic violence isn't about "having the shit kicked out of them" which, in any event, is already covered by other offences such as GBH, ABH etc.
What's more, and I won't quote the myriad authorities on the subject which you can find if you are sufficiently open-minded to Google it, but the incidence of DV in same-sex couples is comparable to heterosexual couples. Current thinking is that most DV is a result of proximity rather than men trying to subjugate women.