I'll be honest, I don't like the term transgender. It's incorrect- it implies our genders cross something when, with the exception of multigender and genderfluid people, they really don't. It works with transsexual in a way- most people do see their sex crossing over to the other. I know a neutrois who now considers itself "transsexed" because it finished transition.
But our language is difficult and trans people aren't accepted enough for me to figure out a viable alternative (although, of course, it's hard to find one that works for everyone no matter what you do). As I mentioned before, my definition for transgender is "an adjective describing a person who’s gender (part or all of it) does not match the sex they were assigned at birth". And I've been thinking about it- and I kind of like the idea of misassigned at birth. I've seen a few trans women say "the doctor should have said "it's a girl"." and, as I've been pointing out a bit lately, not all trans people feel that their body is wrong- just how people perceive them. Misassigned works better for me.
Aside from bodily issues that transsexual deals with, a big problem for trans people is that they were assigned and raised and, in no small part due to this socialization, are still perceived as the wrong sex. It also helps that a lot of people can have issues with the idea of "assigned-____" because too many people assume that it's a correct assignment (doctors know everything, right?). Misassigned emphasises the mistake that was made, that the assignment was not correct.
Like I said- it won't work for everyone. Some trans people don't think they were misassigned. But I hope it's a step in the right direction.