Why is acidic hydrogen peroxide a potent oxidizer?
Just consider the Nernst equation for the half-reaction
$$\ce{H2O2 + 2e- -&gt; 2OH-}$$

You see the potential is clearly pH-dependent. Increased acidity will decrease the concentration of the reduced form, thus shifting the equilibrium to the right and consequently making peroxide a more potent oxidizer.

(BTW, even pH-neutral hydrogen peroxide is far from harmless. It can leave white marks on your hands and gnaw a hole in your jeans, albeit not instantly.)