It was merely an example to explain that brain disorders wouldn't justify mutilation. Just because there might not be a fix doesn't mean we are allowed to do something immoral.

I guess the bizarre conclusion I'm drawing now, as misaligned with the church as it might initially sound, is that a sex change could actually be an exercise in chastity and sexual integrity. How do we conclude here that the brain is misaligned but the body is right, and not the other way around? What is being removed if someone changes their sex organs (aside from fertility in some cases, which may not be an issue in the future)?

Because, simply, brains don't use bodies. Bodies use brains. More accurately, our brains are merely a part of our body. There's not "brains" and "bodies." There are just "bodies," which naturally possess brains. It is metaphysically incoherent to say that my penis isn't for being a penis. My brain is for serving my body and soul. It doesn't have a gendered end by itself. It serves my body, which has a particular sex.

Moreover, the idea of "gender" is a modern one. And it is incoherent for a number of reasons. Take this question. When a man wants to "be a woman" or claims that he "really is a woman," what does this sentence mean? Does it mean he wants to be pretty? Does it mean he cares about having long hair? Does it mean he likes the tv show Scandal? No, it's none of those things. And it can't be. Because men who aren't transgender can have and want all those things too. It means, ultimately, that he feels (he thinks) like people who have vaginas. In which case, "gender" just is related to genitals on a larger scale. Put simply, "gender" just is what we call what people of a particular sex prefer or act. (And certainly, people of a particular sex have different brain structures, so this makes sense.)

If this is true, how could a "brain" be right in the person is a woman, if "womanness" just is necessarily tied to genitals? This is why things like "female souls" and "female spirits" and "female brains" are so important for the transgender movement. But what is a "female brain"? Same answer. A "female brain" is a brain (a particular brain structure) we normally see in people with vaginas. In which case, genitals are still the referent, the thing that makes sex and so makes gender. For, if we saw a brain A and we saw a brain B in a vacuum, why would you call one "male" and one "female"? You would have no rational reason for doing so without a genital referent. In which case, the thing transgenderism is trying to undermine (that genitals define) is ultimately what they rely on to make their case.