A few of the salient points:
1. Rowling and other gender-critical feminists tend to attack an argument that no trans person is seriously making. If you misunderstand (or even deliberately misrepresent) a person's position, that's a bad start.
2. By extension, Rowling seems to frame trans identity as a "choice", eg in a 2019 tweet she wrote "call yourself whatever you please/dress however you like." This isn't supportive, however, because it's mistaking something that is, or feels, innate, for something that can be switched on and off on a whim. Trans people aren't "acting" as trans; they *are* trans. It would be similar to reducing homosexuality to a choice (and then insisting that it's a choice that should be kept private, ie separate from the rest of normal society, which is a homophobic attitude even if it's superficially supportive).
3. It also is often expressed as a "think of the children!" argument: the idea that, if children are exposed to "trans ideology", they might "mistakenly" think of themselves as trans, and so take decisions they'll regret. Framing it this why, transgender identity is something to in a sense "protect" children from. What are they being protected from, exactly? You only need protection from things that are in some sense dangerous.
I suppose what I'm saying is that there's often an undercurrent of transphobia in people who aren't 100% supportive. Not full-on transphobia, but something more subtle: presenting trans people as "the other", who present a threat to established norms, and who therefore must in some sense be curated to ensure that they interact with society properly. But that isn't trans equality. It's presenting a type of person as "a threat until proven valid".