1) Can GC explain what is wrong with what I said above? Can you break what I said down and tell me what's wrong with what I said above and why you disagree with it.

These come down to gender identity. A cisgender man is someone who identifies as a man and was assigned male at birth. A cisgender woman is someone who identifies as a woman and was assigned female at birth.

Cisgender people are people whose gender identity matches their sex assigned at birth.

What if those who don't transition have no such abstract gender identity which just happens to match their biological sex? I am pretty sure that I do not, and my informal surveys suggest that many others don't, either.

I believe that for many people the way the feel about their gender is actually based on their biological sex. For instance, my gender is 'woman' because my body is female. There is a causal relationship which runs from the sex of my body to my gender. In a sense I believe that transgender people do not identify with their biological sex while what the gender identity school calls 'cisgender' people (it's not, really, the correct definition of what many feel) do identify with their biological sex. It affects our lives both directly and in how others relate to us. It is also the basis for sex-based discrimination, sexism, and so on.

In short, I think your definition is incorrect.