So if Doofenshmirtz's mother would never let him swim in public pools, (De Plane! De Plane!) how could he disgrace his family 由 being unable to jump off the high dive (Split Personality)?
In "Split personality, it's sort of a right f passage for a boy to jump off the high-dive, and that is what I think why he was allowed to go to the pool.
Actually, he wasn't really supposed to jump into a pool. I won't tell 你 what it really was, but let's just say that it was only filled with water on alternating thursdays.