In this poem by Nancy Senior, the speaker is ridiculing the sexist idea of "chivalry" as expressed in the person of the man she meets in the forest. Without pausing to consider the fact that the woman may be perfectly happy with her dragon, the man assumes that she must be filled with "fear" and that it is somehow his duty to save her. By intervening in her life, he actually damages this woman by killing her pet dragon. He evidently has not taken the time to assess the situation or to listen to the woman's wishes—she has not had time to "say a word," and the man has not paused to notice the fact that the dragon, on a "golden chain" and docile, is obviously the woman's pet. Instead, he has made a sexist assumption that she needs to be saved.
The idea of the man on a "white horse" is couched here against the fairytale backdrop of the St. George and the Dragon story. It imagines that story from a feminist point of view and asks whether the dragon really needed to be killed or whether the princess really needed to be saved. The poem suggests that it is the influence of stories like this one, which do not take into account the feelings of women, which are responsible for the proliferation of this kind of behavior in men.