It was very nicely shown by an old episode of Nova entitled Why the Towers Fell, which is available through WGBH, by the way.
A fatal flaw in the design of the towers is that the fireproofing applied to the steel structure wasn’t sticky enough, and came off during the impacts. Thus the steel had no protection from the fires and inevitably would soften and fail. In the south tower the tube snapped on one side, whereas in the north tower what probably gave way first were the attachments of floors to the central spindle-like structure, so the antenna tower starts falling visibly just before the sides of the building do.
