To play devil's advocate, I would note that many bats are made of wood; and that "batting" is also a material that's very useful as kindling.

Also, the question is phrased like a classical trick question. It sounds like the kind of false dilemma where, whichever option you choose, an interpretation of the sentence can be made where you chose wrong. So, IMHO, hedging on an answer to that question is likely sensible.

(And that line of argument can be taken further than you'd think; you might think replacing "a bat" with e.g. "water" would suffice... but what if it's a sodium fire?)