Where violence is reciprocal, I don’t think anyone disputes women, tend, to suffer the brunt of the damage.
Perhaps courts are more reliable than surveys, in the sense that more objective evidence is sought, rather than basing their findings solely on claims.
However, I think it’s obvious that violence against men is taken less seriously (and perhaps for good reason to some extent, because women tend to be physically, and even psychologically more vulnerable, but let’s be honest, that doesn’t necessarily mean it isn’t occurring as much or more frequently) than violence against women, and this dissuades men from reporting on it, after all, if a man and women are fighting, even if the woman is clearly the instigator, both male and female onlookers will often come to her aid, even going so far as to attack the man merely for defending himself.
From a young age, boys are often taught never to hit women under any circumstances, and to be tough, not to be a victim.
In all likelihood, the reason why there’s a discrepancy between convictions and surveys is because men won’t go out of their way to on report violence perpetrated against them by a spouse, due to social pressures discouraging them from doing so (‘A woman? Bro what’s a matter for you? Man up!’), but when asked, when given the opportunity and not dissuaded, men will speak about violence inflicted upon them, violence that would’ve otherwise gone unreported, where as females are just as likely to report male on female violence to police officers, as they are to surveyors.
Or, you could claim that men are being more dishonest on surveys than women.
It’s not as if men and women are reporting violence equally to police, but evidence is supports females being victims over males, no the vast majority of reports are from females.
Just because men aren’t reporting it doesn’t mean it probably isn’t happenings, and when you look at the social roles men and women have been assigned by society and are expected to carry out, as well as the physical and even psychological disparities, we should expect men reporting on it far less.