For those of you in Rio Linda - we have both men and women's competitions for the the same reason we segregate smaller boxers from heavy boxers - so we can see a high level of competition from athletes who have risen to be the absolute best that they can be.
Let me spell it out for you slowly: why do we segregate the sexes in the Olympics? Can you handle that? take a deep breath and try.
As for your dodge: yes indeed weight lifting, boxing, have weight classes - why not let all in those weight divisions, men and women, vie for qualification and then if they make the cut compete in the games?
I bet you won't answer.