It's worth noting that Fama has since then walked back on the strong statement of the Efficient Market Hypothesis. I don't know that he ever intended to say beating the market is impossible; rather that beating the market must be impossible, under the rigorously definition of an idealized, "efficient" market.

Unfortunately a lot of proponents of the EMH (especially non-academics) have taken this concept and run with it in ways Fama didn't intend. His position would be more accurately stated as the claim that modern markets are eventually informationally efficient, for any given instance of information asymmetry.

It's a useful model that approximates markets, not an empirical claim about the world.