I think I get what Williamson's overall picture is behind chapter 3.
Williamson argues against Quine, who would deny the synthetic analytic distinction altogether. What I gather from chapter 3 is that Williamson wants to claim the disjunction of (1) and (2).
1) not all philosophical truths are analytic
2) analytic truths are no less substantial (informative about the world) than synthetic ones
If either (1) or (2) is right than philosophical discoveries are no less substantial than any other discovery. So I take this chapter to be a revolt against philosophical exceptionalism about subject matter.
Seperately, he seems to endorse the disjunction of (1) and (3).
3) analytic truths are not known in any special way in virtue of being analytic
If either (1) or (3) is right then the way we investigate philosophical truths is not necessarily different from the way we investigate any other truths. So I take this point to be a revolt against philosophical exceptionalism about method.
He goes on to argue this (though in what appears to be a sort of jumbled way) about modal analyticity, frege-analyticity and direct reference-analyticity. But generally, as pointed out in the chapter, Kripke has a good defense:
A) ~ (analyticity -> necessity)
B) if (A) then (C)
D) ~(analyticity -> a-prioricity)
E) if (D) then (F)
One could deny (B) and (E), but that seems odd. It seems like one motivation for claiming analyticity has a special metaphysical status (of not informative about the world) is because of its correlation with necessity, ditto for its epistemological status and a-prioricity.