The big natural arbitrage opportunity is other people's coarse-grained price changes. HFTs make finer-grained changes at shorter intervals, and so win trades that the exchange directs to the best offer.

If being a market maker is profitable, then this profit derives from executing trades. Because the exchange directs trade to the best offer, the profit goes to whoever offers the best price, which is whoever adjusts its offer prices quickest. That's the recipe for HFT.