@Adelishious
One of the biggest differences between men & women is the difference in interest in ‘people’ and ‘things’. So those who want to be engineers are the people who are most interested in things, that’s why its nearly made up of all men. On the flip side you don’t go into a nursing or care profession if you only care a bit for people it’s those who care to the extreme that want to enter into that as a profession, which is why they tend to be nearly all women.
The percentage of engineers who are female varies by country, and so does the percentage of nurses who are male. Most countries show increases over time in the percentage of women in engineering and in the percentage of men in nursing.
There are many theoretically possible reasons for the dominance of men in engineering and the dominance of women in nursing.
Some that you didn't mention are pay differences, and gender stereotypes about profession as well as about the role of men and women in the wider culture (e.g. if men are expected to be the breadwinners and women are expected to do most of childcare, then men will seek higher paying jobs and women will seek jobs which allow flexibility, even if they pay less).
Then there's the hostile workplace climate women in STEM fields in general may experience, which seems not to happen for men who enter nursing. Indeed, male nurses tend to earn more than female nurses.
I would argue that even this difference needs much more analysis and requires multivariate modeling.
It's also interesting that some people-centered professions are very male-dominated. Politics, for instance, and also most clergy/religious leadership (though here women are also often excluded altogether).
And almost all jobs, in reality, have a mixed job definition involving both dealing with people and dealing with things, though the percentages differ. The military, medicine on the whole, and many service occupations where concrete services are provided for individuals to me seem to have both aspects.
Some very people-centered jobs were almost entirely male in the past (psychotherapists), so it's possible that nursing, for instance, will keep changing towards more equal numbers of men and women.