If, as The Architect states, picking the door to save Trinity will lead to a “cataclysmic system crash”, why doesn that happen when Neo chooses?
It’s likely that picking the wrong door wouldn’t immediately cause the crash, but it would set in motion a chain of events that would cause the crash: Zion wouldn’t be given up, The One’s code wouldn’t get assimilated, the Matrix wouldn’t get reloaded, and the One would prolong the battle, all contributing to the catastrophic failure that would soon follow.