I'm hesitant whether to write this as an answer or as a comment for why this question should be closed as off-topic, since the reasons likely have little to do with economics. Since you did specifically ask about economic reasons, though, I'll attempt an answer.
The economic part of your question is:
What are the economic reasons why, when encountering low pay (or anticipating it at the start of their careers), women should not simply respond to economic incentives, and choose to transfer to higher-paid occupations to increase their earnings?
Yet, the assumption that women don't take compensation into account when choosing a field is almost certainly false. It's just that neither men nor women solely consider compensation when choosing a field and the other reasons are mostly psychological and/or sociological in nature, not economic. In particular, people tend to go into fields that they enjoy, that bring them satisfaction, at which they are adept, and/or that are more likely to have work/life balances matching their needs regardless of their gender or the relative compensation levels of those fields.
While there are obviously both men and women who enjoy almost every field, it shouldn't come as an especially large surprise that those don't occur at equal rates in every field or even in most fields. Far more women than men prefer being school teachers or nurses or doing clerical work, while far more men than women prefer being engineers, airline pilots, or construction workers, for example. A quick look at gender enrollment rates by major at any university which teaches those subjects will confirm this, in addition to data on people actually in the workforce.
For the United States, the U.S. Department of Labor produces detailed statistics on gender breakdown by occupation.
According to this dataset, women constitute 46.8% of the U.S. workforce in 2020. Of the detailed occupations listed for which % female data is available for 2020, only 106 of the 358 had female percentages that were even within 15% on either side of the 46.8% average. 131 of the fields had less than 31.8% females, while 121 of them had more than 61.8% females. Looking at fields within 5% on either side of the average, less than 10% - only 34 - of those 358 detailed fields were between 41.8% and 51.8% female, compared to 159 below 41.8% and 165 above 51.8%
In general, female percentages are incredibly low (mostly under 10%) for occupations that involve large amounts of manual labor and especially heavy lifting. Given the risk involved in these fields, their pay levels tend to be higher than other fields that require equivalent amounts of experience or education. For example, among all occupations in the "Installation, Maintenance, and Repair Occupations" category, only 4.1% of workers are female. In the "Construction and Extraction" (i.e. mining) category, only 4.0% of workers are female. Only 4.4% of firefighters and 17.1% of police officers were female.
On the flip side, for the "Office and Administrative Support" category, 72.7% of workers are female, while "Personal Care and Service Occupations" have 77% females. For "Healthcare Support Occupations" (think home health aids, nursing assistants, and other medical aids, but not doctors or nurses,) 85.3% are female. These fields largely require similar amounts of experience and education as those in the previous paragraph (generally ranging from no experience to trade school, but almost all less than Bachelor's degree requirements,) yet most have much lower personal risk and more personal interaction and/or direct caretaking.
For fields requiring a college degree (Bachelor's, but not Doctorate,) STEM fields tend to attract relatively few females, but have the highest starting salaries of all such fields. Only 16.5% of Architecture and Engineering occupation workers were female and only 25.2% of those in the Computer and Mathematical occupations category. Of the latter category, only statisticians were majority female at 50.3% and the only other groups near the overall workforce average were web and digital interface designers (44.8%) and operations research analysts (42.9%.)
On the other hand, Community and Social Service occupations had 68.8% female workers. In the Education, Training, and Library occupations, 73.5% of workers are female, but the numbers vary dramatically in regards to the age of the people being taught. Post-secondary education is actually pretty equitable at 51.1% female (though this almost certainly varies dramatically based on field being taught, which is not listed in the data.) On the opposite extreme, 98.8% of preschool and kindergarten teachers were female. 79.6% of elementary and middle school teachers and 58.8% of secondary school teachers were female.
Going too far into why women and men, on average, prefer different fields at different rates is not really on-topic here, as it's more a question of psychology or sociology than economics. Those reasons could include innate differences, differences in gender roles taught by society, or, seemingly much more likely, some combination of both. But what is very clear from the data is that men and women have very different average preferences on occupation, regardless of compensation.
