The "Not All Men" thing is highly annoying and unnecessary, as you rightly pointed out.
If you are a man, and you don't want women to shut up, why comment at all?
If you are getting offended by Women talking/writing about issues they face or negative interactions they have on a daily basis then, doesn't it say something about you?
For example, if a man writes an article about his experience with, say, a Narcissistic Woman, I wouldn't comment on it, saying, "How dare you tell your story?" because 1. it's not my place, 2. I don't relate to it at all.
Dear Men, if you are an ally, then, by all means, support, spread, and amplify female voices. If you aren't, then the least you could do is move on and read other articles that are more suited to you.
Defending your gender, well, nothing good can come out of it. All it says about you is that you find something relatable, a similarity between someone else's story and yourself.
Instead of writing a hateful comment, take some time to implore that feeling. Realize something, change something. At worst, learn to ignore it.
After all, who listens to "Women," right? - So let us speak freely.