Here's why the sign is associated with a crab:
* Ancient Greek Mythology: The sign of Cancer is associated with the crab sent by Hera, the queen of the gods, to distract the hero Heracles while he fought the Lernaean Hydra. The crab was eventually crushed by Heracles, but Hera honored it by placing its image in the sky.
* Constellation: The constellation Cancer is actually quite faint and doesn't resemble a crab at all. However, the ancient Greeks saw a crab in the cluster of stars that they named Cancer.
So, the name "Cancer" for the zodiac sign has a mythological and astronomical origin, completely unrelated to the disease.