Why does the MLB pitchers bat in one league and not the other?

In the National League pitchers are treated like any other player and must bat for their order in the lineup, in the American League the pitchers spot in the lineup can be taken by a designated hitter. Since the two leagues have different rules, They go by the rules for the ballpark they play in. If it is in a National League ball park, the pitcher hits, if it is in an American League ball park they use a DH. This applies for any regulation game, regular season and playoffs