Mrs. Wynnes tells the American that there is a snake in the room, and he already knows that milk attracts them. So, he grabs a bowl of milk and places it down without anyone seeing him. He says then that they will play the quiet game to really see who has the most control.
The colonel makes a bold statement by saying that in a crisis, men handle the situation better than women do. Yet, when the snake crawled across Mrs. Wynnes' foot, she showed no reaction and stayed calm.
The theme of this story is that your gender has no impact on how courageous you are. This theme is shown when the colonel mentioned that women are still in the era of jumping-at-the-sight-of-a-mouse and when Mrs. Wynnes shows no reaction when the snake is on her foot. These two events are contrary to each other of being frightened.