Bias is a thing. It always is, and always will be - we're all prone to it. It is human nature to put things into boxes, and to have assumptions and preconceptions. They might be cultural influence, or they might be due to personal experiences, but we all have them.
Gender bias is one of these things, and something that is being discussed a lot. Yes, men and women are different. Some of these differences may be nurture, but there's quite a bit of nature too... and I think that's important to know, and take into consideration.
Men, overall, have a different muscle structure - and accordingly are typically a good bit stronger than women. When I grew up, I was given the impression that women can do everything just as well as men. The intention behind this was, I'm quite sure, to not let me (and the other girls in my age cohort) form the impression that we're in any way inferior to the boys. It had the side effect, though, that I believed for many years that I should be just as proficient at everything as men are or can be... including carrying things or heavy lifting. Ah well. I have carried a lot of heavy boxes over the years, and I can't say that I regret it. However, I've also put a lot of pressure on myself to carry just as much, or perform just as well at hard physical tasks, as the male colleagues, and that is indeed something that I could have done without, in retrospective.
Bouldering actually was the thing that finally made me realise: there are anatomical differences, and I will never be as physically strong as my husband if we're in similar good health. That's just nature.
There may also be (I'd say there probably are) differences in how men and women think. There is, however, no proper reason that there should be so many more men in high positions in companies, and so few women. There's also no proper reason why women candidates for something like the post of Kanzler in Germany should be asked about their children and family, and who will take care of them, and men are not. That is just ridiculous.
Good news, though: These days, that inequal treatment is at least seen, and pointed out, by quite a few people. More good news: Germany is getting a law for a gender quota in larger companies, so that at least one woman will be present in the future if there's more than three people in the top management tier. That definitely is a start.
And to round this all off: Here's an article about gender bias, and how reducing the bias during the selection process has led to a significant change of the gender distribution in orchestras. Including a link to a website where you can test your own implicit biases... which is quite interesting!