Why High Frequency Trading cannot be backtested

The reason is simple: as far as HFT impacts on the first price (the highest one for selling operations, the lowest for buying), in a real environment HFT changes the market.

The impact could be minimal for FX markets, where high volumes of transactions are placed, but exists and has effects. Or the impact could be enormous in local stock markets, for instance, where a "touch" to bid/offer prices changes them, modifying market prices and behavior of other actors.

Market impact could be simulated, but, in this case, we have to backtest the simulation.... an impossible fact by definition.