No, I mean personality. Do you think of personality as something being intrinsically tied to a person?. Is a person's personality ultimately what we think of as "them"?
I think for most people, personality, memory, and physical appearance (especially facial appearance) are what they think of when they're forced to ultimately explain what actually constitutes a person.
Most people consider these things unchangeable because the effort and potential risks involved are, to them, unreasonable to the point of being unthinkable. Extensive therapy, psychological conditioning, chemical experimentation, surgery...
Generally, I think people just don't want to change, but they use the argument that it's impossible to change these things as a defense. Then they fall back on "well no one should need to change themselves".
They're perfectly fine as is, after all. How dare anyone say otherwise? You just have to accept them as they are, and if you can't deal with it, that's your problem.