The Short Version
This is a popular myth that's only partially true. Some worm species — notably planarian flatworms — can indeed regenerate into two complete worms when cut in half. However, the common earthworm, which most people picture when they hear "a worm," cannot do this. Typically only the head end survives; the tail end dies. Regeneration into two individuals is a species-specific ability, not a universal worm trait. The claim misleadingly presents an exception as a general rule.