When someone says "X, not to say Y", do they mean "X, but not Y" or do they mean "X, and even Y"?
Normally I would assume it's the first, but I've seen a few examples where it seems ambiguous. Or maybe it's literally the first, but used ironically to mean the second?
An example (for some reason writers for The Atlantic seem to use this phrase a lot):
In somewhat different ways, Orwell and Larkin were phlegmatically pessimistic and at times almost misanthropic, not to say misogynistic.
Best Answer
You are right: literally not to say means not quite Y, but it is mostly used to mean even Y.
[Edited:] In this case, either the author uses this phrase in an unusual way, or he considers misogynistic an even stronger qualification than misanthropic. Perhaps his line of though was thus: they disliked people in general, and, what is even more salient, they specifically disliked women. I will assume the latter, since they use not to say in a conventional manner in your other example as well, dismissive, not to say derisive. Dismissing something is not as strong as ridiculing it.
It literally means they were misanthropic, and one might almost go so far as to say that they were misogynistic (but one doesn't). The latter is supposed to be an even stronger word than the former; the writer says he will not fully commit himself to "misogynistic" but offers it as a suggestion.
In practice, this figure of speech is mostly used when the writer is quite committed; it then simply introduces a phrase that is even stronger than what came before, without any serious holding back. Not to say is often more or less equivalent to even:
If he did not intend it to be read this way, which I think he did, that means he would have used it in an unusual manner that might be misleading for some readers.