Stupid question, why do frets wear out?
 

With nylon strings not wearing down metal frets why do they wear out?

The frets on classical guitars generally do not wear down the way they do on steel string guitars.

Friction - just takes time - water versus stone.

Nothing lasts forever.
Things just wear out over time.

Stupid question, why do frets wear out
 

If you stay away from bronze and brass wound strings, your frets should last a long time. I stick to plain ole silver plated copper wrap. The copper is softer than bronze, and I would rather wear out my strings. The copper is also softer than the frets, so no worry there. It takes years of metal contacting the frets on a classical to wind up with really bad divets in the frets. I’ve had my current guitar for two years, and play it every day. Zero discernible wear.

I'm not sure that they do wear down, so much as get squished out of shape... as others have said it's a long slow process, even just pressing your finger in the same place time and time again will wear metal down eventually. Something like the EVO gold fretwire which while not particularly abrasion proof, is very distortion proof, and appears to last almost indefinitely.