I believe children are taught their biases. If a child believes girls are smarter than boys, she has been taught this or rewarded in some manner which teaches her that her abilities are better than the opposite sex.
Labeling activities does deter some children from participating, especially if they are familiar with being insulted or corrected when something is deemed too complex or challenging. Adults need to be careful not to push their own insecurities and bias onto their children.
There are too many statistics in some of these articles.