A fallacy is something that is not true.
Only silkworms make silk is a fallacy.
Silk is a natural thread, or fibre.
Spiders produce silk to make their webs.
Crickets, bees, wasps, ants, silverfish, mayflies, thrips, leafhoppers, beetles, lacewings, flies, and midges are some animals that produce silk.
All moths make silk.
Silkworms are not worms. They are caterpillars from mulberry silkworms (Bombyx mori), which are moths.
However, silkworms produce the best silk to make cloth for clothes. They spin a cocoon from their silk.

spider web

spider web

silk web

silk worm (caterpillar)

cocoons

silk dress
Photographer: Martina Nicolls
Martina Nicolls: SIMILAR BUT DIFFERENT IN THE ANIMAL KINGDOM