Why 3rd strike passed ball rule?

I presume you mean "dropped" ball rule.

The rule that a batter can attempt to advance to first base after a dropped third strike was part of the "New York Rules," written in 1845. These rules eventually evolved into what we now know as baseball.

The justification, flimsy as it may sound, was (and remains) that every "out" should involve SOME fielding capability, not just the ability of the pitcher. If that sounds silly to you, then it's 167 years too late to complain.