Fun fact: Women actually can see more colors because our eyes are physiologically different. We're not just making it up.
Other fun fact: As a trade off, men see motion better, which is why men are, statistically, more interested in sports.
No, because even though women *tend* toward more colors and men *tend* toward more motion, there are still variations across the board. It all depends on the exact makeup of your eyes, how many rods and cones you have for detecting light and hue.
It evolved when women (read females) would have to hunt for berries etc and needed to be able to differentiate between poisonous and safe plants. Men (males) have better motion sensing because they needed it when they were hunting. It is likely that these adaptations were present many thousands of years before we evolved into "humans", which is why most other sexual dimorphic species have similar adaptations.
Other fun fact: As a trade off, men see motion better, which is why men are, statistically, more interested in sports.