Gender and Sport

For the literature research paper my group is doing gender and sports. I have always wondered why there are female only leagues. I have always wondered this because any woman from those leagues that you talk to says that women can compete with men, but men are not allowed to enter their league. In golf the men are not allowed to compete in the LPGA but the women are allowed to compete in the PGA. If women can compete with men why are there two separate leagues then. Also why are men not allowed to compete in the LPGA, if women were not allowed to participate in the PGA their would be an uproar about how that is sexism.