neo's purpose is also 2 choose the right door, but he doesn't cos he faces deletion aftawards and has the choice of going into exile-programs choosing to go into exile is the 1 thing that can't be accounted for in program parameters. thus, he chooses the left door instead this time. how was neo able 2 choose the other door? because of his extreme willpower? - even the architect indicated that he'd noticed this "interesting. that was quicker than others".. or more likely, because the oracle upgraded his coding with the candy on the bench. the candy/cookie (from M1) i think was a method to change the one's program. she said he has made a believer out of her - this is quite human-like and perhaps the previous one's didn't accept the upgrade candy, now she has hope... hope that neo will finally choose the other.
another thing, apart from trinity's door number in the hotel or whatever reading 303, trinity-3. could her name also hav some significance to the holy trinity- 1)the father 2)the son 3) the holy spirit? jus a thought.