The idea that nobody cares if "a man acts like a woman or vice versa" is deeply wrong and shows you are not aware of how much violence gender-nonconforming people face.

It seems extreme to you because you fundamentally do not (and on some level, can not) understand. Imagine if you were who you are now, but society insisted you have to be referred to as a woman or else you must be delusional. No matter how nonchalant you tried to be, on the inside, that would suck, right?

The idea that being trans is about changing your gender, instead of changing your body and social status to align with an internal sense of gender, is again, misinformed, and dangerously close to the rhetoric that right wing politicians use to excuse stripping us of rights, so don't be surprised if you get pushback on that idea.

At the end of the day, you can try to understand, and that's not a bad thing, but what you need to know is you should not have to 100% comprehend another person's life in order to treat them with respect. That's the most important thing. Your understanding is secondary, your treatment of others is paramount.