At this point the leading scenario is as follows:
The number 1 engine (mounted below the left wing) suffered an uncontained disassembly, throwing turbine blades in all directions, and causing the pylon attaching it to the wing to fail. Some of the blades also hit the number 3 engine (mounted below the right wing), damaging it significantly enough that it suffered compressor stalls. At this point, only the number 2 engine (mounted in the vertical stabilizer) was delivering full thrust, insufficient to allow the airplane to climb. Because the failure occurred after the airplane had passed V1 during its takeoff roll, the pilots had no alternative but to attempt to climb. V1 is the point at which there is no longer sufficient runway to abort the takeoff and safely stop the airplane.