The best way to read the first part of 2 dogmas is as an attack on the metaphysics of intensions. Logicians make a distinction between the extension of a predicate and the intension of a predicate. Consider a predicate like 'has a kidney.' There is a set of objects which satisfy that predicate, and that set is the extension of the predicate. Some other predicates have the same extension, as, in the classic example, 'has a heart.' The set of objects which have a kidney is identical to the set which has a heart, so the extentions of both predicates is the same. But what it means to have a kidney is different than what it means to have a heart. The meaning of the predicate is called its intension.
So all analytic claims are claims which share not just extension, but intension, i.e. they share meaning. Thus the predicate 'is an unmarried male' and 'is a bachelor' share not just extentions, but meaning, too, i.e. intensions, and because of that the claim 'All bachelors are unmarried males' is an analytic claim. We saw how the Logical Positivists used the distinction between analytic and synthetic claims in their philosophical analysis. But they never show just what these intensions actually are, nor how we can tell when one predicate has the same meaning as another predicate. And as empiricists, this knowledge must either be through logic, or empirical. But Quine in essence shows it can be neither.
Quine exempts from his analysis all truly logical tautologies. Those are statements that are true under all interpretations, from a logical point of view. He also does not object to any explicit definition. So his objection applies only to non-explicit, non-logical assertions of analyticity.
Now the logical structure of 'All bachelors are unmarried men' looks something like '(x)[Bx>(~Mx.Nx)]', where '(x)' is read as 'for all x', and 'Bx' is 'x is a bachelor,' '>' is the material conditional, '~' is the negation, 'Mx' is 'x is married' and 'Nx' is 'x is a man.' Read in its logicese, For any x, if x is a bachelor, then it is not the case that x is married and x is a man.' But this is not a tautology, for we can plug in (interpret) B, M and N in such ways that make it false. For example, if 'B' is 'x is a bat,' 'M' is 'x flies' and 'N' is 'x eats nerf balls,' then the sentence says 'for anything, if it is a bat, then it does not fly and it eats nerf balls,' which is surely false, unless there is something about bats that, really, someone should have told me.
But then it is obvious that all bachelors are unmarried is not known or explained through logic. If not by logic, how? Surely we cannot know the similarity of meaning empirically. If they were known empirically, then we would not know them with necessity or with certainty. A dictionary follows how we use language, and the definitions contained document the meaning of words, but the dictionary could be wrong, and are not necessarily true, or else meanings could never change.
How do we know what the meaning of 'has a heart' is? Answer: only by its extension. But then intension is just a sham, it can carry no philosophical weight. The meanings of predicates are not some entity to be discovered or uncovered. Any knowledge we have of that meaning comes by pointing to the things that have the property, i.e. by exntension. It follows that we can get these radically wrong, as we point to all the red balloons, and say 'balloon.' Then someone points to a red shirt, and we say 'balloon.' We only know what we mean because we have pointed to similar things, but the number of similarities and differences are endless, so we do not know if we latch onto the right similarity, the right difference. So, too, with 'bachelor' and 'unmarried man.' We know these terms by generalizing over the instances we have seen, but we can always be generalizing over the wrong properties.
Except... if we operationally define our terms. If we let how we know whether something or is not of a certain type define that type. Then if the method of verification (or falisfication) is the same, we can know that the meaning is the same. This does not use intensions, but is acceptable by the logical positivists. But can we reduce language, reduce the claims we make in language, to its method of verification? The positivists always assumed the answer was 'yes.' Carnap does is best to show it in his master work, The Logical Structure of the World. But they were wrong to assume it, and Carnaps' works shows vividly why it is impossible. And with that, verificationism, or falsificationism, go out the window.
That story next.