She tries to pull rank by calling herself a Grandmaster after he shows his credentials as a Master. Except, as he points out, shes a Woman Grandmaster, which is an entirely different rank made specifically for women, a rank which is equivalent to the sexless Master rank that the boy holds. If he had a vagina, he would have the same Woman Grandmaster title she does. He's throwing her attempt to shove her rank in his face back in her face. This is an even matchup, and there is no reason for her to act so haughty in the first place.

TL;DR Her credentials aren't actually superior, they are equal to his own.