No she doesn't.
There's only a 1 inch difference in circumference between the men's basketball and the women's. 29.5" vs. 28.5"
Regardless of the size, you still have to shoot it straight. And due to the vast difference in strength, it's still easier for the men to make long distance shots compared to the women.
So you agree the ball is smaller. It also is 10% lighter.
Is the goal the same size?