Takeoff is the worst possible time to lose an engine. The plane is heaviest so the power requirements are at their highest. At the same time, you're faced with low airspeed and altitude. As any pilot will tell you, being low on airspeed, altitude, and power at the same time is a deadly combination.

When a twin engined plane loses one of them on takeoff, it represents more than a 50% decrease in performance. The most crucial performance factor in that situation is the plane's ability to climb. Climb performance comes from surplus power, which is the power above what is necessary to keep the plane in the air at any given airspeed. Suppose that at 200 knots, it took a minimum of 40% thrust to keep an A-300 in the air. With both engines running, 60% of your thrust is available for climb. However, if you've lost one engine, you're down to 50% power available, leaving a surplus of only 10%. The situation isn't helped by the fact that the thrust is off of the centerline, meaning you need substancial rudder inputs to keep the plane straight and under control. That extra rudder input means more drag, making a bad situation even worse. That's why many planes only have at most 20% of the climb rate on one engine that they have with both engines running.

A catastrophic engine failure on takeoff is much worse than an ordinary failure like a flame out or compressor stall. In a catastrophic failure, the engine literally comes apart, throwing hot debris at very high speeds. For example, the turbine and compressor sections on many large engines spin in excess of 30,000 RPM. If you start throwing compressor or turbine blades, the effect is similar to an artillery shell going off near your plane. The wings above the engines are full of fuel and other things like hydraulic lines. As in the case of the Concorde crash last year, bad things happen if you throw hot debris into the wings.

The situation is even worse if an engine actually falls off the plane like what appears to have happened this morning. In that case, the chances of hydraulic failure are much higher. Hydraulics are not only used to operate the control surfaces, they also operate other systems like the wing flaps. Airliners typically take off with the flaps down around 10 degrees for increased lift.

There's a world of difference from losing an engine during cruise or landing. At cruise, you already have altitude to spare. During the cruise phase, loss of an engine means the pilot has to trim out the asymmetric yaw and begin a controlled letdown. It's not a very big deal. If an engine fails on landing, it's also not a big deal because you're already flying at reduced power at a time when you've burn most of your fuel. Lighter weight means less power is required to fly, so your surplus power margin is substancially greater than during a take off emergency.

As for the crash causes, sabotage is one possibility that can't be ruled out without an investigation. However, there are several other possible causes, both natural and man-made, that could've caused the crash. The investigation has barely began. Unless there's a "smoking gun" type piece of evidence found in the wreckage or on the recorders, it could take from weeks to months to know the cause. Coincidental factors count for very little in an accident investigation - actual evidence based on solid science count for everything. The NTSB is very good at this sort of thing.

Even if some terrorist group tries to claim credit for the crash, that doesn't mean they did it. Several years ago, an Air Lauda airliner came apart in midair, killing everyone on board. Some terrorist groups tried to claim credit. However, the accident investigation proved conclusively that a design flaw allowed the thrust reverser to deploy in flight, causing the pilot to lose control and ripping the plane apart.

I suggest you leave the work to the experts. You obviously don't know a great deal about the subject.