I can't imagine why the CA opted to bring the levers back to climb instead of pushing them forward to the TOGA detent when he was first made aware of the problem though.
The takeoff roll and right after lift off is a really bad time to be thrown into an unfamiliar emergency situation. Here are some horrible examples:
Kenya Airways Flight 431
ASN Aircraft accident Airbus A310-304 5Y-BEN Abidjan-Felix Houphouet Boigny Airport (ABJ)
TWA Flight 843
ASN Aircraft accident Lockheed L-1011 TriStar 1 N11002 New York-John F. Kennedy International Airport, NY (JFK)
AA Flight 191
ASN Aircraft accident McDonnell Douglas DC-10-10 N110AA Chicago-O'Hare International Airport, IL (ORD)
Logically the reason the Captain elected to pull the throttles back is because the aircraft had been hinting at that.
Due to attention tunneling/plan continuation bias, it is very difficult to change a plan once it has been set in motion in your mind.