Nice, it took me a while to find the fallacy. (I really hope you did that deliberately, it's masterly.) What you have done is a variant of the observation tha

Nice, it took me a while to find the fallacy. (I really hope you did that deliberately, it's masterly.) What you have done is a variant of the observation that within any family the sisters have more brothers than the boys, except that you averaged over 100 families to make the effect more subtle. But if you make the towns larger, the discrepancy will disappear (for example at 100 towns of 50k families I would expect it to be lost in the noise).