The Green Knight's lady is Gawain's fiercest enemy because she offers the greatest temptation to his reputation as a noble knight. While a knight is expected to face death and physical danger, it is much harder for Gawain to face a sexually tempting woman. He is left alone with the woman for a good period of time and sees her in bed. She tempts him with her beauty.

The girdle she gives him is also a great temptation. The girdle is not only an intimate piece of clothing, distinctly feminine, but she also claims it will allow him to save his life when facing the Green Knight. Essentially, it will allow him to cheat both the Green Knight and death. This choice brings Gawain the greatest shame in the end.

So, while the wife is not physically dangerous, she injures Gawain's sense of morality. He tests his integrity and he fails.

When it comes to the rules of knighthood, knights strictly follow them in order to maintain a respectable reputation among the people, other knights, and as representatives of the king for whom they serve. Examples of those knightly rules are explained in the story of Sir Gawain and the Green Knight as Gawain bows, kisses, and maintains his "courtesy," or manners. However, when Gawain's foe is a woman who does not have to follow the rules of knightly engagement, Gawain is at an inexperienced disadvantage. Gawain later compares himself to Biblical men like Adam, Samson, and David who were also weak in the presence of women, but who stood strong against traditional enemies of war.  So, the Lord's wife was fierce because Gawain didn't have any training to combat "women's wiles."