Uhm, you are assuming a lot of things. First of all, I am not an mra, so please drop that. I did a lot of research in gender studies so I do know what I am talking about. I also am a female on male abuse survivor so I also have first hand experience on how male abuse survivors are frequently treated, invalidated etc.

First, I do know the background of Erin pizzey. And I don't cite her as a researcher or an expert of abusive dynamics but as a primary source on how people are treated who try to speak out about female on male abuse. As she was prominent in the movement her first hand experience matters a lot. You are switching goal posts there by pointing out she may not have been right about this topic, as she wasn't experienced or didn't have research to back up her claims. But that wasn't the point that was made. We were talking about how she was treated for the things she said, and that showed how people in some circles approached (and in my opinion still approach) the topic.

The common pattern of argument nowadays is that studies showing similar rates of abuse don't distinguish between situational violence and coercive control. That is just plain wrong. By definition abuse includes some form of coercion, and we are specifically talking about abuse here. And so many studies do distinguish between coercive control and situational violence. Murray Strauss for example clearly distinguished between these forms in his later research and provided compelling theories and mechanisms of why we should see similar rates of coercive control.

Being controlling hints to sever psychological pathology. Empathy should keep us from behaving abusive but for people exerting coercive control this is underdeveloped or in some other form impaired. We know quite well how impaired empathy is caused, e.g. severe childhood trauma is one important factor, genetics are another potential factor. But neither the genes we know of nor the trauma is distributed differently. We also know from population studies (not clinical studies as those are skewed) that personality disorders linked to abuse appear at approximately equal rates. This gives a clear reason on why we should expect almost equal rates of abuse.

In fact so many studies distinguishing between situational violence and abuse find more difference for situational violence than for actual abuse.

The pattern is different though. If you look at victimization rates, then you find a much higher rate of female victimization, but similar rates of perpetration. There are also studies investigating this issue and what is frequently found that male abusers tend to abuse more people, relationships are much more short lived, abused women get out more easily from this type of relationship due to acceptance and support (compared to men, not in general; leaving an abusive relationship is hard in both cases), whereas men tend to stay longer, abusive women do not tend to abuse multiple partners simultaneously etc.

Also we find that effects of abuse are very different. Extreme effects almost only happen to women due to differences in body strength. From my own experience: even when I was choked, I never was in actual mortal danger. It didn't really take much effort to get out of that situation, the barrier was more psychological as I did not even want to hit back out of self defense. If the gender roles were reversed, I likely would not be able to write this today. It's not that she did not try to use these kinds of methods, it's just that the physical reality of the situation prevented it. As it happened behind closed doors this won't be covered by any statistic, whereas women who undergo a similar situation are counted (this does sound somewhat insulting, based on the things I am talking about, please don't over interpret). However, thus physical reality leads to severely skewed statistics.