Henry Veatch, in his book Intentional Logic: A Logic Based on Philosophical Realism, gives several arguments to challenge the notion of analytic truth. Here’s an excerpt from Chapter 3, "Mathematical Logic and Intentionality," in which Veatch is trying to show that the analytic propositions, which are certified by reference to the meanings of the terms used and require no reference to experience or to matters of fact, cannot be defended:
Everyone is familiar with Kant’s celebrated examples of the two different types of propositions. Thus, as he thought, “Every body is extended” is clearly analytic, whereas “Every body is heavy” is just as clearly synthetic. Unfortunately, in contemplating these examples, we cannot but wonder whether, if Kant were a successful teacher of philosophy, as no doubt he was, he actually followed the now current practice of the profession of ever inflicting upon his students his own ideas and theories. It has been my experience that although professorial expositors of Kant do not seem to have too much difficulty with his examples of analytic and synthetic propositions, students, particularly if they be comparatively unsophisticated, almost invariably do.
Thus they will insist that to them “heaviness” is just as much a part or what they mean by “body” as is “extension.” If the professor counters with the suggestion that they would never have known that heaviness pertained to physical bodies, had they not observed them to be heavy simply as a matter of fact, the recalcitrant students are likely to respond that they would never have known that extension pertained to the very notion of body without having observed physical bodies to be in fact extended.
In short, however sound the distinction between analytic and synthetic may happen to be in principle, it would seem to be extremely difficult to apply in practice. Nor will it do to try to make the distinction clearer by suggesting that analytic propositions are those which are a priori, whereas synthetic propositions arc empirical. As we have already noted, it is the distinction between the analytic and synthetic which is usually offered as a criterion pf the distinction between the a priori and the empirical. Other wise, how can one be sure that a given proposition really is a priori and not based on experience? To be sure, one might have a sort of feeling or “hunch” that certain propositions are a priori. But hunches, particularly among philosophers, are notably unreliable. Hence there would seem to be no other definitive criterion of a priori certainty than the fact that in any a priori proposition the predicate must be presumed to be contained analytically in the subject.