As with many odd rules, softball has it's roots in baseball and follows many of it's conventions. When baseball was first played, all the bases were "centered" on the four corners of the diamond, like second base still is today. As the game evolved, the rules changed.
If you go back far enough, in baseball batters could reach base on "foul hits". When the rules regarding foul balls were changed, the rules about a batted ball hitting a base had to be changed, too, since first and third base were partially in both fair and foul ground. To remedy this, first and third were repositioned into the diamond, so that they rested entirely in fair ground.
Second base wasn't moved, as it's location had no effect on the "fair/foul" rules. Home plate, which was originally a square, had the corners cut off to form the familiar shape we see today, thus making the plate entirely in fair ground.
Despite what some might say, this all happened a little bit before my time! First and third base were moved inward in 1877. When ASA wrote the first official softball rule book in 1933, that base placement was retained, copied straight from the existing baseball rules of the day.