Why do women pay less for car insurance than men?

Because of statistics. Insurance companies use statistics to help determine how much risk is involved in issuing a policy to a person, and the data show that men are more expensive to insure.
It's not that men file more claims than women. Actually both genders file about the same number of claims. The problem is the nature of the accidents involving men are different than those involving women.
Women tend to drive more slowly, so when they are involved in an accident, there is less damage and repairs will cost less. Men tend to drive faster, tend to drink and drive more often, and consequently have accidents that cause more extensive damage and greater injuries. This costs the insurer much more to fix, so the premiums are higher.