"Man" and "woman" are archetypes. Not descrptions of objects, like "table" or "chair" -- instead, like "hero" or "villain" or "aristocrat" or "scoundrel."
All of us have an archetype we identify with; some of us have a physical appearance or characteristics that don't match the archetype we identify with. Some of us feel that it would benefit our mental health to have our physical appearance match more closely with the archetype. Among other things, it makes it so that other people are more likely to see us as us, rather than seeing a person who isn't us.
Not being seen is deeply traumatic. If one's physical characteristics cause them trauma, those characteristics should be considered disabilities, and we should welcome resolutions to them from medical science.
Some of us identify very strongly with one of "man" or "woman," others more weakly. Some of us are in between somewhere, or switch back and forth depending on the day. Or don't identify on that gender spectrum at all, or in some other dimension not represented by those two points.
That's why we call people what they want to be called. I'm not going to pretend that it's easy to get your lizard brain to really see some of us as "men" or "women" when the physical appearance doesn't match our expectations. But just using the correct language goes a long way towards communicating that you want to see them, and by extension, reduce their trauma.
Now that you know this (and of course, if you agree), you must grapple with the fact that misgendering people is traumatic (which is to me a reminder to try harder every time), and that misgendering people on purpose is simply cruel.
Side note, I made a point through this comment to refer to us instead of the more arm's length "some people, other people, these people, those people." We are some people, we are other people, these people, those people.
A_A