I couldn't tell you exactly why there is such a rule in the first place, but I can give you a little background on its origins.
As with almost every rule in softball, this one has roots in baseball. From the earliest days of baseball the rule has always been that a batter is out when the third strike is caught by the catcher. By extension, if the pitch was not caught, the batter was not out.
This isn't a very good reason, but's that's just the way it was! Why do we get three strikes and not four? Why can't runners advance on foul balls? How come there are four bases and not six?
These are coventions dating back over a hundred years that evolved as the game of baseball evolved. When the first official softball rules were published in the 1930's, many of the rules were copied directly from the exixsting baseball rules. Eighty years later, we're stuck with the odd "third strike rule".
Often generically refered to as the "dropped third strike rule", the rule doesn't require that the catcher actually drop the ball. Rather, the rule applies when the catcher does not legally catch the ball. "Catch" in this sense is defined exactly the same as the catch of a batted ball by a fielder for an out- the ball must be airbourne from the pitcher's hand until caught by the catcher. If the ball bounces and is then secured, it is not legally "caught" as required by the rule.
While the rule has been around longer than dirt, the times when the rule applies was changed as baseball evolved. In the earliest days, the final strike had to be caught no matter the number of outs or if first base was occupied. It didn't take long for teams to exploit this rule to their advantage.
Suppose there are runners on base at least first base. Catchers could purposely not catch the third strike, forcing the batter to run to first and the other runners to advance. By purposely dropping the ball, the defense could earn cheap extra outs on force plays that would not have been there if the ball had been caught and the batter had been out.
Along the same lines as the Infield Fly Rule, baseball came up with exceptions to the uncaught third strike rule to protect the offense from deception by the defense. The exceptions are that it does not apply when there are less than two outs and first base is occupied or anytime there are two out (regardless if there is a runner on first base).
With less than two outs and first base occupied, the catcher could gain extra outs by purposely dropping the ball as described above. To prevent that, the rule became that the batter cannot advance to first in this case. The batter is out- catch or no catch of the pitch- so there are no force outs to be had and nothing for the defense to gain by purposely dropping the ball.
With two outs, even with first base occupied, purposely dropping the third strike would be, well, stupid. Catch the pitch and the inning is over. Thus the exception about first base being occupied when there are two outs. The rules still require the catcher to complete the play by securely catching the pitch.
There have been several books published about baseball rules from the early days and maybe one of them has a better explaination of why this rule came to be in the first place.But I do know that this 19th century relic of a rule still has folks scratching their heads in the new millenium!