“Normal” is a statistical term represented by the following graph: 
This kind of distribution can be found along many dimensions of human experience — height, weight, intelligence, etc. The people at either end of the graph, the 2.5% people, are called outliers.
I have heard a number of comments over the years along the lines of:
“I just don’t get gender roles. I never felt like I fit in, or was accepted as a girl. But I don’t feel at all like a boy, either.”
“Gender never made much sense to me, and when I first learned about trans identity, I wondered if that could be me. But it’s not. My hormone balance doesn’t bother me, nor does my body, or being called he.”
The people who made these remarks to me are outliers, but not in the realm of gender. One was much shorter than average for adult female. Her life experience sounds familiar to many who transition and aren’t able to be seen as their intended gender. She said to me: “People just can’t get past my height to treat me like a person, or really hear whatever it is I’m saying. I’ve found in work situations, it’s easiest if I meet people when we’re both sitting down, so they don’t immediately know I’m a foot and a half shorter than average. It’s easier for some people to get past my height in that situation, so that later, they’ll treat me like a person. But even then, some people never can get over it.”
The other person was someone whose intelligence put him in the realm of outlier, a cisgender male with an IQ of about 180. He said: “My experience of the world has always seemed out of synch with everyone around me. I never fit in when I was young, school was a nightmare. I have a musical soundtrack to my life, for instance, that gets me weird sideways glances when I try to explain to others. I’ve learned never to say what’s really on my mind, it just gets me in trouble. I’ve had people assume I was schizophrenic, hearing voices or some such, when I tell them I hear music and see colors surrounding my daily life. I joined Mensa when I was a teenager, figuring that was the only place I might find girls I could date who might not think I was crazy.” (Mensa is an organization for the super-intelligent)
The roles associated with “man” and “woman” are not only defined by gender. Fitting in as a man or woman in U.S. society also depends on not being an outlier on any number of dimensions. Those who are not “normal,” in a statistical sense, don’t have an easy time fitting in as men or women, regardless of the reason for their outlier status. While innately unfair, this thought can provide some comfort to the trans person who has grown up believing their experience of not fitting into gender roles was unique to them.
