"They want to leave this country."
I'll just point out that "他" has a person radical, and is a good candidate for depicting the neutrality of the sound "ta". Also, as a third-person pronoun, it's really not about self-identification, but about description by the writer.
The writer who coined "她" was a male who used it in his poetry, and many see it as a product of Western influence. There were feminist writers' groups both for and against its adoption in the early 1920s.
Prior to that, there were other problematic ways to render "she" in writing.