"the claim that a man can become a woman by saying s/he is a woman"

Who has ever made such a claim? There are people, certainly, who are unhappy with the gender assigned to them at birth. The point is that they are neither men nor women. Some have an innate desire to be one or the other. Fortunately medical science is able to assist them to reach the gender they aspire to. That does not make them someone to be feared or impugned.