This argument - which dates back to a 1980 paper by Joe Stiglitz and Sanford Grossman - is as follows. If markets were informationally efficient, nobody would have any incentive to analyse corporate information, because by definition doing so wouldn't yield any return. But if nobody looked at such information, it would never get into share prices, and so markets would be inefficient. If rational people believed markets were efficient, therefore, they wouldn't be efficient. Efficiency requires that investors are irrational - that they go to the bother of analysing information, even though it is pointless to do so. But this contradicts the assumption behind the efficient market hypothesis, that investors are rational.
However, I'm not sure this argument has much practical relevance, simply because it's easy to believe that, in the real world, people are sufficiently (moderately) irrational to chase information even though it is futile to do so.