I think if you look physically, then there is a difference between the genders. Some professions, the female are more ideal and some professions, the male are more ideal. They can't be equal trait vs trait, i mean when it comes to strength, its male, but when it comes to kindness and affection, i think its the female, so that is why i believe that female can be more successful and more useful in professions like teaching and related jobs, but men can be more ideal for jobs where physical strength matters. No point in taking it as a gender inequality.
It is funny you mention jobs which take physical strength, because in reality little women actually seek to take part in those jobs were men are over presented because being strong and having a high stamina is a requirement. When feminist organizations talk about gender inequality they never mention positions like construction workers, plumbers, lumberers, etc. they mostly talk about positions in the head of corporations, CEOs, bosses, managers, among other similar positions of responsibility, where men are also over represented.
There is some hypocrisy in those talking points in my opinion, if those feminist organizations would actually find equality they would also encourage women to also join the military and enroll in the defence of their country, but it is not how they are trying to push their message forwards.
Also, you talk about women are supposedly better in jobs which require kindness and care. Still it is common to see men in jobs of nursery and as teachers.