I don't agree with the gratuitous swearing, but I share your confusion!
The phrase "trans-[fe]male" is totally ambiguous; but it applies to members physically of either sex who feel emotionally of the opposite.
The murkiness of the whole situation is summed neatly by its accompanying piece of illiteracy - using the noun "transition" as a verb. (The verb is "to transit", meaning to cross.)
I do not understand the drive because I do have it - so how can I understand it?
Instead I understand that some people have that drive, emotionally, to be as far as possible of the opposite sex.
Some people are born with "anomalous" genitals, including vague, infertile hermaphrodism; but I think most who wish to change their sex are physiologically completely of their natal sex.
Sadly, they become their "new" sex only in appearance. Surgery and hormone treatment give them the general appearance they want, but also neuters them. Though I suppose that is not a problem if they do not want children anyway.
What does annoy me, is not such crossed-sexual people wanting respect for their emotional needs. That is fine although their actions sometimes raise real problems such as using toilets and changing-rooms in work-places and sports-halls, and participating in competitive sports.
Rather, it is that some want treating as if a special case, with "needs" and "rights" above and beyond those of everyone else. No they are not "special", or above everyone else; and they need understand and respect that in some situations their demands do make others around them very uncomfortable.
Nor, and this probably applies only to a few of them, do they have any civilised "right" to launch ugly campaigns on the Internet and elsewhere - "death-threats", forbidding lectures, etc. - against anyone who even just points out the obvious, that a sex-change operation leaves you neither female nor male biologically. Such attacks are bullying, so childish and cowardly.