I consider myself transSEXual because it is the SEX characteristics which cause my dysphoria and which I need fixed.
The term transgender is useful politically but a problem socially because cis people assume I have an issue with gender roles and expression, which I really don't.
Dysphoria really comes down to SEX characteristics because those are what is different between males and females, so having a male brain in a female body, SEX and SEXUALITY are the problem, not anything else. All the other aspects of my personality and life are do not belong to one gender or another in our 21st century society!
As an American, I hate to talk about sexuality in any way, of course--it's a taboo subject! But I did desensitize myself somewhat by coming out as gay years ago. Sexuality has broader impacts in your life--like your choice of partner--which necessitates talking about it, even in a euphemistic way. Just being totally honest, most of the emotional/personality change with testosterone centered around sexuality (that and it affected my mood disorder profoundly, which is to be expected since I am trans). And what is different between men and women? Well, some muscle growth, some skeletal ratios, and, oh, sexuality! Sorry, we're stuck talking about this, taboo or no!
To the OP, I reject the notion of chromosomes as all wise and all knowing. You are disregarding intersex people and chimeras, as well as the fact that the male gene can jump out of the Y chromosome in some cases meaning there are XY females and XX males. So not only is this quite silly, it's also essentialist and in a sense wants to say that people like us don't exist. Because we are MIXED in our sex characteristics. That's the whole problem. The whole disease in a nutshell. We have masculinized, unmasculinized, or partially masculinized brains and our bodies don't match. This is not about gender, man or woman in society. It's about sex--male or female. You could have dysphoria about either one, of course, but only dysphoria about SEX is treated with hormones and surgery--get it?
If society makes you dysphoric, change society. If your body makes you dysphoric, change your body. Gender is undergoing a state of massive flux here and now. But bodies are the same as they ever were.