My parents do not wish for me to study any professional degree (engineering or business) since they don't want me to work in any private firms. The only fields I am open to are medicine or to work as a teacher. They say that living with them I cannot work anywhere except the option given to me but once i am married then I can do as my " husband" wants.
I do understand that working in a non-muslim country especially for women is difficult but living in(removed) which specially caters to Islamic moral codes I don't understand the problem my parents see. And if there is something wrong according to the islamic laws then how no way out of this does it become fine once I'm married.
I dont want to fight with my parents but I see no way out of this. Is it Islamically wrong for a woman to be career oriented? How should I try to convince them?

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As per se it's not haram for a girl to work outside her house in any firm or institute as long as she abides and follow Islamic law and doesn't face any bad and evil intentions from na mehram. Suppose you work in a company or institution or any office and you abide the shariya, but the namehram over there keep a disgusting and bad eye upon you
then you should quit