Take-off is the single most stressful time of a flight, as far as the engines are concerned. It's almost universal practice *[1] to use maximum power to minimise runway use, especially since the pilot must use whatever runway is left to slow down if he decides to abort take-off. In addition, turbofan engines (used in almost all large airliners) produce considerably more thrust at sea level than after a few thousand feet of climbing.
It's entirely probable that a crack in the engine mounting widened and failed at this point, perhaps in turbulent air as well as the normal take-off stress. It's the kind of thing regular maintenance is supposed to prevent, but which is inherently unpredictable and, very occasionally, goes wrong.
It's the airborne equivalent of blowing a tire on the highway, and is in fact much rarer - the reason it makes the news is that so many people get hurt at once when a plane crashes. Note that engine *failure* is fairly common - dealing with such a thing is part of a pilot's training - but having it actually drop off is rare. When it does, it very likely affects the structural integrity of the whole wing, not to mention the balance of the aircraft.
*[1] - Some engines can't be run at maximum power safely at sea level, mostly high-performance piston engines.
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