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The most prominent critic of the distinction is Quine. You can read about the reasons for his opposition here. A quote:

Quine... offers a diagnosis of the persistence of the concept of analyticity. Philosophers find the idea plausible because they tend to assume, sometimes unwittingly, that there is a clear notion of cognitive meaning which relates each sentence to the experiences which count for it or against it and which can be applied to sentences taken one-by-one. Given that sort of notion of meaning, we could say: the synthetic sentences are precisely those to whose truth or falsehood experience is relevant; the analytic ones are those whose truth or falsehood is wholly independent of experience (and which can therefore be known a priori).

Quine criticizes this idea of atomistic (sentence-by-sentence) cognitive meaning.... Quine invokes holism, the idea that most of our sentences do not have implications for experience when they are taken one-by-one, each in isolation from the others. What has experiential implication is, in most cases, not an individual sentence but larger chunks of theory. Holism, Quine claims, undermines the atomism of atomistic cognitive meaning.