Softball was first played in 1887 as a recreational activity and it was actually first played as a side activity to a Yale vs. Harvard football game. Here, it was a makeshift softball (a balled up boxing glove) and the handle of a broom as the bat, and it was soon thought of as a great way for baseball players to train in the winter: indoor baseball. This provided an alternative to traditional baseball, and subsequently something for men to assign to any women that might have wanted to play baseball. The game rose in popularity with women and then in 1953, Britain saw its first women's softball league come into commission. Then in 1996, women's fastpitch softball saw the Olympics for the first time.
Because of the presence of baseball, softball, being the one that was discovered second, had been assigned to women, in adherence with our patriarchal world. In this way, men have always played baseball, and women have always had softball, but the two are not that different. Much of the difference is baseball pitchers throw overhand and softball pitchers perform an underhand toss, yielding a different range of pitches that either sport can throw. For example, in baseball, there does not exist a "rise ball" as there does in softball.
This coexistence does not mean softball is only a sport for girls, after all it did start off plainly as an alternative to baseball, favoring no gender. There are countless ameteur and high-level co-ed and even all-men softball leagues. So, no, softball is not only a sport for girls, it can be played by men and all genders, in fact it was started by men.