My disagreement with the authors of the Times article is partly in their claim that "sex assigned at birth" has somehow entirely replaced (or is meant to entirely replace) "sex." The former doesn't replace the latter.

I also disagree with the authors that the term "sex assigned at birth" exists primarily to accommodate and soothe trans people's feelings.

There's room for both terms — "sex assigned at birth" and "sex" — they can mean different things, depending on context, including the identity and motive of the person who uses them. The nuance (as with any word) is unique to each instance when the word is used.

I believe I said all of this in my article, or at least I tried to.

The authors (Byrne and Hooven) actively make a variety of anti-transgender arguments. I alluded to this where I said they've been on this topic for "years," but I did not attempt to get into the larger context of their agenda, as then my article would have been much longer. (They each have a book, for one thing.) They are claiming that trans people deny (or want to deny) the existence of sex, and that trans people do so primarily driven by personal feelings about gender, and this is just not really correct. It's a straw man argument. They make this argument in the NYT, not for no reason, but because it slots into other anti-transgender arguments they make. The NYT routinely publishes this kind of poorly substantiated anti-transgender rhetoric, as I've discussed in about a dozen articles on Medium, and so this article is also serving a particular agenda of the newspaper.