It's less what they say you can't be, and more what they say you can be. Because of these aforementioned gender roles that society still perpetuates, the jobs children are pushed towards are different. There's been an improvement in recent years, but you'll still see that there's a gender divide even as children between jobs, and a lot of it seems to be based around gender stereotypes. Boys are more likely to want to grow up to be athletes, firefighters, astronauts etc. etc. while girls are more likely to want to grow up to be doctors, teachers, scientists, and chefs/bakers. It's also worth noting that, despite more girls wanting to be doctors, there's twice as many male doctors compared to female doctors in America. And female doctors performing, on average, better than male counterparts.
Basically, biology should be playing a minuscule amount in representation within a field. All genders are equally qualified, it just appears that the societal narrative steers genders into different fields.
I feel like I should pipe up here.
These stereotypes that society has around gender roles (which you say is the societal pressure pushing people to pick jobs), where do they come from? Like most stereotypes, they're rooted in reality. In this case, rooted in biology. Instead of biology playing a small role, biology is playing the directing role.
I don't think it's controversial to say that stereotypes around gender roles have weakened significantly in the past half century. That said, the underlying biology the resulted in those stereotypes is still present. Our biology hasn't changed, but our society has. So boys still wanna be firefighters, girls still wanna be teachers.
Like I said earlier, I reckon that our unconscious biological pressures are more influential than societal pressures nowadays.
tldr; gender role stereotypes are just a manifestation of biology
Even with a root in biology, how accurate can some of these notions be considering how long ago they might have been formed? I can understand saying only men should be soldiers back in the day when war consisted of wielding swords and spears and required a large degree of physical strength. But saying only men should be soldiers today, when war has largely been mechanized and the skill set required to wage war is different from before, begs whether our notions about biological differences may need to be changed because of how the roles themselves have shifted.
This also doesn't hold up with more modern roles. For example, I mentioned that a larger percentage of boys want to be astronauts compared to girls. This is a job that has only existed for less than a century, and is largely a field that is devoid of any specific trait that benefits a specific gender over another. Why is it more boys would want to be astronauts compared to girls? You could say it's because boys are more adventurous, but is it really that simple? Girls are just about as curious as boys at a young age, and biological differences between genders are much more muted at younger ages, so it would stand that interest in exploring space should be somewhat represented among girls. It seems more likely that the most lauded astronauts of our time have been male, and the role itself has been typically typecast as a male profession. As such, girls don't take interest in the job because the job isn't presented to them as an option due to lack of representation or perceived opportunity.
It also fails to explain why more girls than boys want to be doctors, yet there are more male doctors than female doctors and there are more female nurses than male nurses.
take a guess
If a woman believes they are paid less for the same job, in the US AUS and UK (these are the countries I know it exists in not the only countries the law is present), there are laws in place so that the woman in question can take it to court and get what she deserves its illegal to pay people differently because of their gender.
Hoe exactly do you think clothing colour affects the development of a child? I dont expect the child to understand why their parents put them in blue or pink clothes, and I also dont expect it to affect their development much. Stereotypes are unavoidable, the average person from culture or gender x does thing y more often than the average person from gender or culture z, therefore the stereotype among gender or culture z is that culture x does thing y.
What gendered treatments other than clothing do you think are common? How do they affect the child?
In modern schooling the path is not narrow, from when you first start the teachers say you can be anything you want to be if you work at it. They also dont treat boys and girls differently. Girls are not brought up to fill job x or told they cant fill job y.
Also you seem to be skirting round all the questions asked - "I think everybody can be qualified for any job given the right training" doesnt answer the question "do you think that men and women are equally suited to all jobs". You also didnt answer any of my questions, youre writing well written short essays that dont answer the questions posed.