All the ingredients existed in the towers (aluminum and rust) as well as the energy required to ignite it (the gravitational potential energy of the buildings).
This type of a reaction is nothing extraordinary; like many other materials, most metals will burn (oxidize). Rusting metal is the same process as burning, only it happens more slowly.
Here's a quick and dirty estimate of the amount of energy present in the towers:
Mass: ~500,000,000 kg (each)
Average Height: ~210m (total height = 417m)
gravitational potential energy (joules) = mass*height*g
= 500,000,000kg * 210m * 9.8m/s^2
= 1.029x10^12 Joules
So, how much high explosive is that equivalent to? One tonne of TNT (tTNT) is equal to 4.2x10^9 Joules. Thus:
tTNT(eq) = 1.029x10^12 J / 4.2x10^9 J
= 245 (=tons of TNT) = 0.245 kilotons
To put that in perspective, the smallest nuke in the US arsenal is ~0.3 kilotons and the largest conventional weapon (the MOAB) is a mere 0.011 kilotons.
All the "truthers" neglect to mention this when they say that the fires in the towers weren't enough to cause steel to melt and thermite to ignite. While it's true that the jet fuels and office contents weren't enough, the buildings themselves contained more than enough energy to melt steel and ignite thermite.