Also as others have mentioned, we don't know what information the Pilot had from his instruments. The tower can say you have a fire, to which the pilot will reply I know, but the extent isn't always known in the cockpit. The AA DC-10 accident was mentioned before, the pilots of that plane actually thought that they had merely lost the engine, ie. the power from it, neither the tower or cockpit ever mentioned the fact that the engine had separated from the wing.
So to say, why didn't he stop is something we can't answer from here. the assumption is that he was past V1, but until the flight data is interupted, lets not question the motives of either ATC or the cockpit crew.
Aircraft I've flown: A300/A310/A320/A321/A330/A340/B727/B732/B733/B734/B735/B738/B741/B742/B744/DC10/MD80/IL62/Bae146/AR