In any culture, girls are not considered to be good at chess, or any mind-blowing activities. Why do we encourage girls to play chess?
I won't discuss those orthodox reasons here. I will show you some reverse thinking why you want to let your daughter play chess.
Comparing to boys, with fewer participants, girls can easily excel at chess. They can achieve very good results quickly. Good results of course provide positive feedback, and will motivate them to get better. For a boy to feel achivement, he needs reach 2200. For a girl, 2000 will make her outstanding.
Smart girls are not nerdy. They are actually very popular. Chess not only trains them how to think, but also helps them learn how to make friends and how to handle all kinds of social activities. Unlike math or science, chess is hard work combined with play, so chess girls can have a lot of fun.