Kirk wasn't silent.
He said, "No it isn't. And you punished and tortured me because of it." That's textual agreement with Lester that it wasn't fair that Kirk's world of starship captains doesn't admit women, full stop. Kirk's agreement even spans two sentences (at least in that transcript).
Infer away, if it floats your boat. Your choosing to read Kirk's reply as somehow referring to Lester's situation as being unfair instead of what Lester said was unfair is such an inference.
Incidentally, I'll happily concede that, in general, not everything is intended to be read literally. What's specifically getting me here at this moment is that the claim that there's only a single line in the episode asserting that Kirk's "world of starship captains doesn't admit women" is flat-out wrong. Kirk's reply asserts it as well. If you're going to explain away Lester's statements as the ravings of a madwoman, then you'll also have to explain away Kirk's statements in reply as not just remaining silent, but outright lying, or going along with her if you like, to try to placate her.