"The deadliest aviation disaster" has at least four correct answers, because the question hides a choice about what is being counted.
Deadliest accident: Tenerife, 1977
Two Boeing 747s collided on the runway at Los Rodeos on Tenerife on 27 March 1977. 583 people died. This is the answer to the question as most people mean it — the highest death toll in an aviation accident. It involved two aircraft on the ground, in fog, and no mechanical failure at all.
Deadliest single-aircraft accident: Japan Airlines 123, 1985
A Boeing 747SR suffered an explosive decompression after a repair to its aft pressure bulkhead failed, destroying most of its vertical stabiliser and all hydraulic systems. It flew on for 32 minutes before crashing into mountainous terrain. 520 of the 524 people aboard died. Four survived.
Deadliest mid-air collision: Charkhi Dadri, 1996
A Saudia 747 and a Kazakhstan Airlines Il-76 collided near Delhi on 12 November 1996, killing 349. The accident drove the adoption of airborne collision avoidance systems in Indian airspace and accelerated their spread globally.
Deadliest event involving aircraft: 11 September 2001
The attacks of 11 September 2001 killed nearly 3,000 people using four hijacked aircraft. They are not usually counted in accident statistics because they were not accidents, but any honest answer to the question has to note them.
Why the distinction matters
Each of these records produced different changes. Tenerife rewrote radio phraseology and created Crew Resource Management. JAL123 rewrote structural repair oversight. Charkhi Dadri accelerated collision avoidance. September 2001 reshaped cockpit doors and airport security worldwide.
It is worth noting what all of these have in common: none of the technical records has been broken since. Tenerife stands after nearly fifty years, JAL123 after forty. Air travel has grown enormously in that period, and the accident rate has fallen faster.