Not only that; Cortana picked him (Noble 6), not Chief. Cortana never explicitly states she chose Chief. Never. Her ability to cooperate with a Spartan was once tested with Chief (I think), but that was temporary. She never directly chose him, ever.
I don't think anyone understands how subtle Bungie has crafted Halo's storyline which is inferable even only by campaign cinematics' dialogue, without any terminals or books. Noble 1 - 6; they were all to die.. in order, from 1 to 6, despite Noble 6 being Cortana's actual "chosen one". Chief is 7 -- Bungie's lucky number, the real chosen one by (ahm) the Gaurdians, precursors or whatever the fuck
One more statement: Yes, 343i has fucked halo up.