The basic answer is we don't know, hence why this is such a contentious issue. There are many known physical[1] and psychological[2] differences between the sexes[3]. Boys tend to play with inanimate objects while girls tend to play with dolls and role play. Women tend to be more social, while men are less so. Men with higher testosterone tend to be more aggressive overall[4]. Some think many of these differences are caused by society, while others think that it has to do with an entire chromosome being different, causing differences overall.

[1] https://en.wikipedia.org/wiki/Sex_differences_in_humans

[2] https://en.wikipedia.org/wiki/Sex_differences_in_psychology

[3] These differences are based on population distributions, and there are plenty of outliers within those distributions, eg. masculine women, feminine men. I am speaking of averages here.

[4] https://en.wikipedia.org/wiki/Testosterone#Aggression_and_cr...

See https://slatestarcodex.com/2017/08/07/contra-grant-on-exagge... and read the first couple of comments as well which is further back and forth between the two authors.

You are trying to verify an innate property of a person by measuring the emergent outcome of their choices. While this is a good litmus test, I do not think the answer to quantifying this acclimation toward a certain profession is something that can be measured discretely.