Reason's that show Sir Gawain is courageous.

When Gawain and the servant travel through a somber, snow-covered landscape, and at the top of a hill, the servant stops and begs Gawain to reconsider his mission. He warns that the Green Knight is a horrible, cruel monster: huge, merciless, someone who kills for pure joy. The servant begs Gawain to run away; he would not tell anyone. But Gawain refuses to run, as that would prove himself a cowardly knight. When he continues on his journey, we see his true courage.