When the Green Knight issues his challenge, everybody in King Arthur's court at Camelot hangs back. The Green Knight begins to mock the court, causing Arthur himself to step forward, ax in hand.
At this point, Sir Gawain intervenes, offering himself instead. While we might expect him to base his claim on his great strength or courage, he instead argues it on the basis of his unworthiness, saying his life is the least valuable of any. He states he is the "weakest" and has the "feeblest" wit. He also notes that his honor comes not from his own accomplishments but from his status as the king's nephew. He also says that he should be allowed to stand in for Arthur because he was the first to ask. Gawain says, too, that this "folly" should not fall on the king:
I am the weakest, I am aware, and in wit feeblest,
and the least lost, if I live not, if one would learn the truth.
Only because you are my uncle is honor given me:
save your blood in my body I boast of no virtue;
and since this affair is foolish that it nowise befits you,
and I have requested it first, accord it then to me!
As events will show, this is false humility on Sir Gawain's part. He actually believes he is a chivalrous and worthy knight. Later, when his life is on the line and he is tested, he behaves dishonorably, withholding the truth of the green girdle from his host. It is only after his adventures with the Green Knight that his limitations as a person become real to Gawain, who returns to Camelot chastened and wiser.