In "The Use of Force" by William Carlos Williams, what is the extended metaphor used?
The language used in "The Use of Force" by William Carlos Williams tends, like the language of his poetry, to be simple and direct, eschewing such literary devices as metaphor. The incident is described in quite simple, literal terms, with the reader seeing how the need to examine the child causes the doctor to overpower the child with force, in a manner he himself finds distasteful, both because he is a generally kind and humane person and because he does not like the way the act raises in him primitive and violent emotions.
Although there really isn't an obvious extended metaphor in a strict sense, we can see the notion of a struggle of wills as a central and quasi-metaphorical theme, with the narrator imputing to the young girl a strong will and steely determination, and describing the the incident as a "battle" of wills. Since the doctor does not have access to the thoughts of the young girl, we have no actual idea of what is going through her mind.