Well IMO I think its hard to say whether boys or girls as a group are actually better at maths.
I don't think your thinking is particularly straight. She will not have to "out compete" the boys. The only person she will have to compete with is herself and the standard that is set. And if she is good enough to make the standard that is the only issue, what the rest of the world do is irrelevant.
It seems like there are more men at high levels in maths than women (or at least from my experience). Whether that is because men are better, or whether there are social issues impacting the number of women in maths is harder to establish.
Even if you believe that men are better than women at maths, there is clearly significant overlap in capability, otherwise the difference would be immediately obvious and provable.
If you assume like a lot of things that "maths capability" is normally distributed, and the peak of the curve is say a few % less for the women group than men (completely hypothetical), it still means that a woman at the top of the female distribution will outperform the vast majority of men, in a similar manner to the fact that the top women marathon runners will outperform the vast majority of male marathon runners even though men as a group are faster.
I think the fact that your daughter really wants to do the subject despite the "persuasion" otherwise indicates she is really keen on it. If she is really keen on it then she obviously likes it, is probably good at it and will work hard at it and should be encouraged to do it, not dissuaded.
Have you discussed it with her tutor to see what they think ? I do think a lot of maths skills are innate rather than taught, and teachers should be able to see whether a student, either a boy or girl, has the ability to make it to the highest level in the subject.