This sort of an issue is the one that seems to bring out the fact that many of us live in different worlds.
For me sexism is not a reality of my daily life. My partner and I have deep mutual respect and we support each other physically and mentally as well as we can, especially now that her brother is very ill and she spends a lot of time in the hospital with him. She works in a supportive and warm environment (mostly female but she gets along very well with the men there too). My working environment is not exactly warm but quite fair and reasonable. She is a strong and active woman, a great organiser with a talent for getting things done and done well. Besides her job and managing the family, she is involved in several community projects, swims and pursues her hobby of pottery. I have never heard her level an accusation of sexism at me, but of course we do have our usual little male/female minds gripes (usually to do with cleaning and organisation, or lack thereof in my case).
Our little daughter is growing up to be an active and inquisitive kid. She likes her dolls but she also like the duplo, riding around on her bike and scooter and generally keeping up with her older brothers.
I don't see patriarchy at work in our little world. But I have seen it elsewhere, so I am not denying the possibility that other women are suffering from sexism.
What has been unfortunate in this episode at DW is the broad brush and hateful approach to it, which to me indicates that people are smarting from their wounds and resentful at men in general. In private I would just say "I am sorry" if confronted with this sort of stuff, but in public it has to be challenged because as a statement of fact, it is unfair to men and unfair to leave it unchallenged.
So a public forum is probably not a good place to get things like these off your chest. It just comes across as an attack and of course people get defensive.
Women here may well have legitimate grievances and I am sorry if they had been mistreated. Hope we can heal enough to see that not all men are sexist and deserving of being scorned and put down. And that the male gender as a whole is not evil.
On the other hand it can be important to acknowledge the biases that are at work in some parts. It's all part of healing together.
I guess I am speaking as one who has had to deal with a fair bit of hurt and prejudice myself, having grown up in a Jewish family in a hotbed of anti-semitism that is the Ukraine, at a time when the memories of massacres like the one at Babi Yar (where 33000 people where killed in a single operation assisted by local collaborators) were still fresh. Should we have harboured hatred towards Ukrainians while living amongst them? We knew a family that had risked their lives hiding their Jewish neighbours during the occupation. They got no fame or reward after the war, nor did they expect any. Later I shared house with some German exchange students here in Australia and we did talk about it all. It is not easy, but holding on to the hatred is even harder I found. But healing does take time and above all the courage to open up to it all (the pain, the disappointment, the guilt, the hate) and the strength to let it go.