SCULLIBUNDO
Banned
It's supposed to be awkward because the Chief could do nothing. He was outside of his comfort zone - he was losing his comfort zone.
Consider the alternative: Chief half shrugging and cocking his head like a six month old would only make the scene seem condescending on Cortana's part. Like she's talking to a child, not an indoctrinated soldier. His plead was the best he could do, and in his steadfast refusal is the player supposed to sympathize.
You won't change my mind that the scene was written really clumsily. It was over the top with melodrama so rife it could have been on daytime television.