Yo no sé la razón por la que él fue allí.

English Translation

I don’t know the reason why he went there.

Would be helpful if the reason were explained, i.e. why it’s not “para.”

The speaker uses the word razón, i.e the reason or cause of the persons action; I find it helpful to think of por as meaning ‘for what reason’, and para as meaning ‘for what purpose’. Alternatively, if the speaker were saying, Yo no sé el propósito, I’d expect para … to follow.