I don't know how true it is worldwide, but at least in the United States, baseball and softball are very gender based, and it seems like it has been that way for quite some time, although not always. Why did such a sharp, cultural division come about with this sport, as opposed to others such as soccer or basketball, which see both genders playing essentially the same sport, instead of women pushed into a similar, but distinctly different, mimic of the "Man's" game?
I'm afraid the answer is based on some dated thinking. Softball was invented by and played by men initially in the late 1800s. It was originally called indoor baseball, and the term softball didn't come until the 1920s. Softball was initially a slow pitch game, with the space between bases being shorter, the field being shorter, and the ball being quite soft and larger than today's softballs. The first softball was supposedly a boxing glove. Because of the general ideas about differences between sexes in the late 1800s, people believed that softball was more suited to women than baseball. Women thus began to form leagues to play softball and the popularity spread. As female leagues grew, softball was seen increasingly as a female sport, whereas baseball was a male sport. As the idea that women are physically frail has subsided, softball evolved into the fast pitch game that is played in competitive sports today. Slow pitch is now generally reserved for casual leagues of men, women, or coed hobbyists. Incidentally, there have always been baseball leagues for women as well. During World War II, women played professional baseball while the male league lost its players to the war. Baseball just does not have the widespread popularity for women to play that softball does.
It should also be noted that the game of baseball was not quite the same game that is played today. Players did not use a glove until the 1870s. Pitchers also threw the ball slow underhand. It was supposed to be thrown like you were "pitching" a horseshoe. The game was more of a high scoring game with more play in the field. A lot of people will mention that the idea of the day was women were fragile. However keep in mind overhand pitching wasn't sanctioned by the baseball commission in the late 1800s due to the fear of injury to the catcher. When they did start throwing overhand the pitching speed was limited by the ability of the catcher to handle catching the ball. Playing defense in a game without a glove or any protection was not for the faint of heart male or female.
Within 8 years of softball being invented, West Division High School Chicago formed a women's team and by 1899 they had their own coach. A lot of people point to an issue of Spaldling's indoor baseball magazine in 1904 which dedicated an entire section to women's softball teams which peaked the general publics attention. Like baseball, as safety equipment got better, the speed of pitching increased. The attitude of the time was that sporting athletics were for men. Softball was one of the earliest sports in which women were able to break that glass ceiling and play. EDITED - For spelling and formatting