Why do bears have hairy coats?
Why this joke works
A Bear’s Hairy Coat
Fur protection sounds like for protection, so the answer gives a sensible purpose while naming the material that serves it. Coat already applies both to clothing and to an animal's covering, helping the two-word ending feel natural. Give fur a little emphasis without stretching it into a different word. The joke works best when the response sounds almost too practical to be a punchline.
A closer look
An answer that almost stays factual
Unlike a riddle that produces an absurd explanation, this answer stays close to reality. Warm covering really can be protective. The amusement comes from expressing that reasonable idea through a substituted sound. This makes it a gentle first pun for listeners who may not yet enjoy elaborate setups or fictional disasters involving the animal.
Fact behind the joke
Two kinds of polar bear hair
Polar bear fur includes a soft undercoat and longer, coarser guard hairs. The two layers help keep the animal warm. The joke speaks about bears broadly, but this specific example shows how a hairy coat has structure beyond a single uniform layer of fluff.