DV is a very complex legal minefield. I have years of working with defendants. I would say that a majority of DV complaints are valid in some way, and that many times the DV goes both ways (but it's rarer for the woman to get charged, even if the instigator).

The biggest issue is that once the perpetrator is removed and/or charged the victim often petitions the prosecutor and police to drop the charges. The prosecutors I know will generally not do this and will push for a guilty plea or trial. It's hard for the prosecutor to know whether the victim is being manipulated into asking for the charges to be dropped, and regardless, a crime has probably been committed, and in the justice system the plaintiff is the state, not the person who was battered. This can lead to a stand-off where the victim refuses to come to trial to testify, and where the prosecutor has a Hobson's Choice of whether to arrest the victim and jail them until trial to get them on the stand or let the case drop.

DV cases are hard.

Cites, please? A quick skim of the literature doesn't support this and I'm dubious, but I'm willing to be proven wrong.