I was just reading this article by journalist Conor Friedersdorf, complaining about how Canadian psychologist Jordan Peterson is being unfairly treated by journalists, who try to twist his subtle anti-feminist arguments into crude anti-feminist slurs. He certainly has a point. But then one comes to comments like this
[Interviewer]: Is gender equality desirable?
Peterson: If it means equality of outcome then it is almost certainly undesirable. That’s already been demonstrated in Scandinavia. Men and women won’t sort themselves into the same categories if you leave them to do it of their own accord. It’s 20 to 1 female nurses to male, something like that. And approximately the same male engineers to female engineers. That’s a consequence of the free choice of men and women in the societies that have gone farther than any other societies to make gender equality the purpose of the law. Those are ineradicable differences––you can eradicate them with tremendous social pressure, and tyranny, but if you leave men and women to make their own choices you will not get equal outcomes.
20 to 1? That seems really high. For nurses and for engineers. So I decided to do something rude, and check the numbers. For nurses, I found these statistics. There’s a lot of variation in Scandinavia. In Denmark it seems like about 20:1 female to male. But in Norway it’s 9:1. In Iceland it’s 100:1. Looking further afield, in Israel and Italy 20% of nurses are male. And in the Netherlands nearly 25%. This does not look like an ineradicable difference to me. It looks like path dependence and social context.
What about engineers? Here Peterson is, to use the technical term, talking out of his ass. There is no country in the EU with such an extreme gender imbalance for engineers: The most extreme is the UK, with about a 10:1 male to female ratio. In Sweden it’s 3:1, in Norway 4:1, and in Denmark 5:1. In Latvia the fraction of female engineers is up to 30%.
I think, if you want to make provocative “I’m just trying to be rational here” public arguments, you kind of have an obligation not to make up your supporting facts.
Common Infirmities 
This is extremely biased. Without even mentioning the cherry-picked data, you did not even quote Jordan Peterson verbatim. He said (at around the 13:45 mark) that, “…Scandinavia it’s 20 to 1 female nurses to male, something like that, it might not be quite that extreme…”. Very convenient for your narrative that you left it out. Feel free to check for yourself. The link is given below.
As you might have noticed, I linked to a transcript, and quoted the transcript, which left out the phrase “it might not be that extreme”. I stand by the claim that “20 to 1, something like that, it might not be that extreme” is a misrepresentation of a number (of engineers) that ranges from 3:1 to 5:1.
Assuming these numbers are correct, in percentages that’s still roughly 75% female nurses and 89% male engineers in Norway. I was actually looking this up because 20:1 seemed like a huge difference to me too but it seems possible looking at these figures that Peterson did an average of the minority gender workforce according to professional sector of all Scandinavian countries put together and expressed that as a fraction. Also, according to your own source the highest number of male nurses is in Saudi Arabia (30%+) possibly one of the most inegalitarian societies regarding gender which would fit with Peterson’s diagnostic. These may not seem like ineradical differences to you and that would be a subjective argument but the numbers here would support that more egalitarian societies have bigger gender differences relative to professional sector and vice-versa. (Also if I may a little constructive criticism, don’t insult the person you are criticising because it makes it harder to take you points seriously and makes it look like you have an agenda however well the argument may otherwise be formulated)
I was looking up these numbers because I thought a 1:20 disparity was huge too. However looking at the figures you give it seems possible that Peterson calculated the average career disparity related to gender of all scandinavian countries (Hence why he says Scandinavia and not a specific country, he tends to be very precise with his words) and put that in the form of a fraction. I noticed you put Italy and Israel’s stats in the form of a percentage, that percentage as a fraction is 1:5 which means there is actually less difference in professions related to gender in Italy and Irael than in the scandinavian countries you listed. Also according to your own source the country with most male nurses is Saudi Arabia, a country renowned for it’s unequal treatment of men and women so this would fit with Peterson’s theory. Even if the differences don’t seem ineradicable to you and even if they weren’t as great as Peterson said (I’m not convinced they aren’t), they are more prominent in those countries which have strict egalitarian social policies than in most European ones so by your own admission that isn’t the way to go if you’re looking for equity (I don’t know why you would want that though, the scandinavians seem pretty happy and it’s not because every sector has a 50% men-women ratio).