==Ash Lines Require Balance==
Ash lines don't necessary prevent the Man in Black from crossing. Instead, the lines enforce a notion of balance. The man in black (evil) cannot cross an ash line if the other side of the line contains people who are very good. This is why the man in black could not cross the line into the temple while Dogen was alive, because the line was in balance. Once Dogen died, the man in black could cross the line. Think of "good" and "evil" people as exerting "pressure", Without a good person inside the circle, there was no good "pressure" and evil was free to enter.