Step 1: Most rectal cancers evolve from adenomatous tissue, so the lesions with the greatest danger are those that flood the bowel with adenomas.
Step 2: The classic precancerous lesions are villous adenoma, ordinary adenomas, and familial polyposis. Familial polyposis is an inherited syndrome in which countless adenomatous polyps line the colon and rectum and almost inevitably turn malignant if the bowel is not removed, so it is the chosen answer.
Step 3: Be aware that option B, FAP, is simply the full name of the same familial polyposis disorder, so the two options describe one entity, and option A is taken as the key.
Step 4: Juvenile polyps are hamartomas with minimal cancer risk, and a lone adenomatous polyp, while premalignant, poses much less risk than the widespread familial syndrome.
\[\boxed{\text{Familial polyposis}}\]