I’m not sure it’s an example that that was the wisest to use but your daughter is incorrect, factually speaking. And you probably should explain this to her and why.
As others have said it is not a universal fact that girls or women can do any job. It is your daughter’s belief that girls/women are capable of doing the anything a man or boy can do. Morally, as well as on an intellectual basis, I would absolutely agree with her (with a few very specific exceptions). But it is NOT a fact that they can, it IS an opinion that they should be able to do so.
There may be legislation to attempt to ensure equal rights for women (and other protected characteristics) but that is not to say that it is a fact that this happens nor that just because something is an accepted norm in this country that it is the same the world over.
I think it is important to be able to tell children when they are incorrect. ‘Having strong beliefs” does not = “I’m right” and it’s important to help children (and especially those with strong beliefs and/or a tendency to be a little dogmatic”) to understand the world is not black and white, their view is not always fact and that whilst something perhaps should be a certain way, the reality is that it isn’t.
I do think there is far too much of a tendency not to criticise/correct children, and to over praise in general. Strong beliefs can be good, a sense of what injustice is and the desire to right those injustices can be good. But inability to acknowledge that you might be wrong (because you’re always praised and admired for your strong beliefs, and never seriously challenged, for instance), or lacking an understanding that other people are entitled to a different opinion and that neither of you are (demonstrably) wrong, is not a good thing. This is how we get the issue with people only willing to be within the echo chamber of those who share our own beliefs. It can fire deliberate ignorance. I think it is far better to be able to have a discussion where you can state your own firmly held beliefs, but be open enough to listen to others and mature enough to admit when you haven’t got all the answers.
At 14, I would expect to be able to have a debate with her along the lines of “ I know you feel strongly about what the teacher said, and you are right that in most instances women should be free to do whatever job (or at least nearly every job) that a man can do, and vice versa. But the reality is that this is not the case. Even in this country where there is equality legislation, there is still bias and discrimination against all sorts of people. And it is also absolutely true that across many cultures and in many countries women absolutely cannot do whatever job they want. So, your teacher was right- it is your opinion that they should be able to do any job, but it is not a fact that they can”. Skirting round it, not wanting to say she has not 100% right because you don’t want to dent her confidence and “I just love that you have strong beliefs” actually does her no favours, if she is not able to evaluate facts to inform her strong beliefs. Strong beliefs are, in and of themselves, not necessarily praiseworthy.
We need to teach young people how to think, not what to think. How to evaluate evidence, how to distinguish fact from opinion, and how evaluate sources, and so on. Otherwise we end up with “false news” and “alternative facts” positions. Whose proponents also very strongly believe that they are right.