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it would be impossible to measure this and prove it because of all of the different factors that you cannot control for. Even if gender does make a difference, it can't possibly out-weigh all of the other factors that play into intelligence.
The only way to argue this is by having an exact definition of what intelligence is. Is it a one-dimensional value? Are there different kinds of intelligence? How do we measure it? As-is, the word "intelligence" has no clear definition so we cannot prove the claim. High risk of Equivocation fallacy
Gender is not biological sex. The correct word would be sex, not gender.
The brain is proven to be influenced by hormones, why is it absurd to think that being in a certain gender might give one a small advantage.
Intelligence cannot be measured
This is untestable. Even if we had a way to measure overall intelligence effectively, you certainly couldn't isolate gender alone as a variable. Even then, it's unclear whether gender here means biological gender, or gender roles, or both.
Boys and girls are treated differently by their peers and other members of society, thus developing differently.
differences in average IQ between men and women are small in magnitude and inconsistent in direction
There is a difference in IQ distribution between the genders. There are more males with very high or low IQ, whereas females tend to have an IQ that is closer to average with less deviation from the middle.
Intelligence is largely genetic and conditioned through exposure to new stimuli. Knowledge on the other hand can be affected by the gender.