The story you were told is false. Ants don't eat wood. Most ants are predators or scavengers, and some have evolved symbiotic relationship with certain fungi.

The story you were told is false. Ants don't eat wood. Most ants are predators or scavengers, and some have evolved symbiotic relationship with certain fungi. Dead wood is degraded mostly by fungi, because other organisms lack the enzymes required to digest the polymers that make wood hard, called lignin.