Firstly the hippocratic oath literally has the following line:
"I will remember that I remain a member of society, with special obligations to all my fellow human beings"
Their productive role is fullfilled by helping patients, not by sitting at home cooking meals for their husband or cleaning.
Secondly your whole argument is based on the principle that women are unable or incapable of doing the same jobs that men can do. I dont understand what basis this has since women are capable of fullfilling nearly every job role within modern society, can you even name me a single common profession which women are incapable of doing?
First things first. I know the hippocratic oath because I am a final-year med student. Not bragging about it. But being a doctor does not mean you are helping patients 24/24 7/7. The oath is regulating the medical practice, as in working and taking care of patients. It does not apply off-call or if you are using the restroom. Doctors have personnal lives as well, and have special obligations towards themselves and their families too, not only patients. An unemployed doctor has no responsibility whatsoever about any patient in the hospital, but can help people in the street in case of emergency for exemple. But using the oath as a pretext to imply that all doctors should work regardless of their personnal lives or choice is a transgression and is limiting the freedom of human beings which they are before even they become doctors. We often neglect that they have basic rights like everyone in society. You went for the special case of physicians because it is easier to manipulate and force them to do things for the 'freater good'. Doctors are paid to do a function that is treating patients. If they do not they are not paid, but they are still doctors because they have the certification.
Second, there are many jobs out there that only men can do, ie. heavy construction work, soldiering, commando ops, firefighting, police SWAT, blacksmiths, car mechanics. Basically most dirty, heavy-duty, and hard jobs are dominated by men. You may find some
females, but they are an exception, not the rule, and those who do these kinds of jobs are not brilliant at what they do. They do it only because they are forced or desperately need a job or just to brag about it being the first female mechanic or special operator in the media of course. And these women are more like men in their behavior, speech, and never feminine and modest women. This pattern is present even in the most egalitarian societies in the world ( scandinavia). Listen to what the canadian PhD Jordan Peterson says about it in youtube. He is a clinical psychologist and studied the phenomenon for more than 25 years. It remains a disparity between men and women even if society is egalitarian, because women will never be men and vice versa. You cannot force it. Listen to special ops colonels speaking about female recruits crumbling under pressure. The women existing in SOF community joined it only because of political pressure from above and the relaxation of physical standards, otherwise they would never have maked their way to there. Some jobs are better suited to men, some are better for women. Simple, but not many people seem to understand it. It is exactly the same as telling us that men cannot be baby-sitters or nurses. There are, but only a minority, and we should agree that these jobs are better suited for females. I would rather go out and rob people than being a baby-sitter even if paid $10 million per day. This is my nature you cannot blame me. You cannot give a female 60Kg and ask her to march 16km in 4 hours. She won't finish the first miles before having stress fractures and quitting. To feel it better, let me say that you cannot give your mother or sister or wife 60Kg rucksack to complete a 16km forced march at 3 a.m in limited time, or are you okey with it? You are then exposing them to an unnecessary risk. I would rather to let my sister cook something than causing her a herniated disc. Watch stories about women rucking with male soldiers, that females end up distributing all their rucksack content for male soldiers who end up with significantly more weight in their rucksack, just for women to go light so they complete the march without needing a hospital, and only male soldiers suffer from this, because they cannot do the same for women. The US military is a perfect exemple that demonstrates the failure of the equality ideals. Their decision to include women in combat positions is motivated by political gains, not by efficiency. Soldiering is just an example. And yes, women cannot do it efficiently. Enjoy!
It is reckless to give women, who are our mothers sisters and daughters dangerous jobs such as firefighting, soldiering, SWAT, construction work where severe injury or death risk is high. Imagine if we do and pregnant women get killed or injured. It is just an unnecessary waste of human resources.
Any job that requires physical strength favors men. Women will never reach the same level as men. The most weight that a woman has ever lifted as I recall is 260Kg. Plenty of men lift 300Kg, and a few are north of 450Kg. These are facts that should not be overlooked. Women have other more strong points such as verbal abilities, empathy, caretaking, memory... that is why patients treated by female doctors have better outcomes than those treated by male doctors ( study published in the BMJ if you are curious google it). Totally natural and should never disturb anyone knowing his place in society. Have a nice day.