Maybe I'm missing a lot of the important media, but I haven't seen what you're describing. Which are the media outlets where you're seeing a fight and push for pretending that biological differences don't exist? Even the original article states that there are differences. Could you provide some examples so that I can see what you're seeing?

Most reasonable people that I know, of either gender, understand that the average man is physically stronger than the average woman. That's a clear distinction. But, lots of other traits are not clear at all, even though they are implied without good evidence. And, in most or all cases there is enough overlap in ability (e.g. the strongest woman is much stronger than the weakest man)

As others mention, the issue of gender rights that I see is one of opportunity and access. The question that's raised is whether the culture imposes biases, implicit restrictions and even punishments when there should be none.