Why Does Steel Wool Burn?
Steel wool burns because it is made up of lots of thin strands holding atoms that come into contact with oxygen in the air [1]. The surface area is small relative to the volume, so the oxygen rich environment helps the steel wool to burn [1]. Metals don't burn easily because the atoms are tightly bound together, not easy to get oxygen atoms close enough to bond to the metal atoms [3].
Steel wool burns because it has lots of thin strands holding atoms that can come into contact with oxygen in the air, making it more difficult for heat to dissipate. A block of iron, on the other hand, does not catch fire because the surface area is small relative to the volume. The heat gets dissipated to many other iron atoms. [1, 2]