We have men's and women's categories in shooting because men also beat women at those. Any sport that is physical will always be like that.
The only reason why we don't have male champions in things like artistic gymnastics is because of old fashioned ideas of sort of movements are manly and which are "more suited to the female nature".
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Skeet shooting used to be mixed in the Olympics. Then a woman named Zhang Shan won it in the 1992 Barcelona Olympics. After her win the International Shooting Union barred female athletes from competing against male athletes. The following Olympics split male and female skeet shooting, but there weren't enough women, so they didn't have any female skeet shooting, so Zhang Khan, the former Olympic champion, wasn't able to compete at all in 1996. The subsequent 2000 Olympics did see the women's skeet shooting.