OK--too make it simple......pilot applies power to a set amount. This amount may be less then max/TOGA, if the aircraft is lighter than maximum. Pilots calculated take off speeds and power setting (below max) with the wrong weight (lower than actual).
So the speeds were set for a very much LOWER weight than the aircraft actually was. AT rotation time the aircraft did not fly because it was too heavy for the weights being used.
At some point pilots realized there was a problem and applied TOGO/MAX power.