If our self-perception includes traits that we do not possess, there is some precedent for society to correct us and tell us that we are wrong. In the above example, TSA would surely inform John that his height, weight, date of birth, and facial features all appear to correspond to those of John Smith, and that he is not, in fact, Bill Miller.
If I attempted to identify myself as a doctor, society would step in to correct my misrepresentation, since I do not possess the certificate of completion for medical school that would make me a doctor. If I attempted to identify myself as a lawyer, the same thing would happen, as I have never passed the bar. If I attempted to identify as a was hero, the government would point out that I had never served or been decorated. In all three of these cases, I would probably face criminal prosecution for representing myself as something other than what I can be proven to be.
What about traits that are more difficult to quantify, like intelligence, or race? In today's world, populations are mixing more widely and frequently than ever before, and the ethnicity of any given person can be difficult to guess. Even so, Native American tribes have standards of proof that must be met before someone can be admitted to the tribe. You may tell others that you identify as Native American, but unless you meet the standard of proof, the tribe will disagree.
If I told others that I were intelligent, but did not speak and act as an intelligent person would, people would probably disagree with my self-assessment. In some scenarios, they would probably allow me to believe as I choose but would decide for themselves that I am wrong. If my intelligence were of importance to my role, however, they might be forced to correct my self-perception. For instance, if I applied for a position as a math teacher but lacked the ability to do basic arithmetic, the interviewer would be justified in telling me that I am not sufficiently intelligent to assume the role for which I am interviewing.
I think by now you can see where this line of thought is headed. If a person identifies with a group that is defined by observable traits that they do not possess, do they really belong to that group? Recent news stories would suggest that they do not. Consider Rachel Dolezal, who identified as black despite being demonstrably white. Consider illegal aliens who identify as being legal residents. Some Americans are positively outraged by such false assertions.
Now let me close the loop. For thousands of years, the standard of gender identity was simply our biology. If you possessed a female anatomy, you were a female. If not, you weren't. Our society has made certain allowances for people that feel different than their biology to live as a gender other than their biological one. But we have not established a standard of proof.
Now that we have allowed people to contradict the existing measurable, verifiable standards of gender, we need to decide on an acceptable standard. To avoid this uncomfortable conversation is to allow sexual predators the opportunity to gain inappropriately intimate access to members of the opposite sex by claiming to be something that they are not. Without standards, we are placing business owners in a position of being legally prohibited from throwing a wolf in sheep's clothing out of the women's room because he claims to be a woman.
Since society seems to be headed toward a place where anyone can claim to be anything and there is no accepted standard of proof, I would like to take this opportunity to tell you all that I identify wealthy. And handsome.