Here's the stalled, unfinished email I never sent to my uncle:
It's possible to explain cancer as a failure of error correction - a spelling mistake, or more accurately, a fateful series of spelling mistakes in the genetic growth program. You could imagine perfectly fictional monks in your cells transcribing ancient tomes of incantations. Most spelling mistakes are caught, others are harmless, but a few, compounding on each other, create a Sorcerer's Apprentice (or "gray goo") spell of runaway growth, namely a tumor. The tumor is sometimes obviously chimeric, with tissues from different body areas growing inside it - teeth, skin, gums, hair, cartilage, etc. That's the kind of tumor that was recently removed from me, anyway.
It might also be illustrative to compare cancer to drug-resistant bacteria. Chemotherapy is similar to antibiotics in the analogy, only it breeds resistant strains of your very own cancer (strains) awfully quickly. The reason seems to be that, as Bebs says, cancer cells mutate faster than normal, and chemotherapy mutates them faster still, while quite brutally getting rid of any cancer variants that aren't "fit" to survive it.
Another idea that can help explain cancer is "contact inhibition," which is the jargon for what cells normally do when they're growing and they bump into each other: they stop growing. Cancer comes from mutations in the growth program that disable contact inhibition. The affected cells begin growing where they shouldn't. If they happen to have mutations that prevent the immune system from noticing and destroying them (either step), I believe the situation is sufficient to call a "neoplasm" or benign tumor. Maybe Beba can comment if any of this is inaccurate. For the benign tumor to become malignant, it's generally necessary for the cells to coax new little blood vessels to grow like tiny roots from the nearest existing blood vessel and carry in more nutrients, and then for some cells to detach and spread to distant locations. But most growth creates new blood vessels anyway. As for how difficult it is for "neoplastic" cells to acquire the ability to detach and spread to new organs through the blood stream or lymph stream, I have no idea. Once they begin migrating, though, which is the definition of malignancy, they still have to get past the immune system, which is more active in blood and lymph, particularly against solitary rogue cells. If you can prevent the surviving (and now definitely immune-resistant) solitary cancer cells from stimulating new blood vessel growth in their new locations, you can often prevent a new tumor (malignant by virtue of the cell type) from becoming dangerous. Unfortunately that's one of many ideas for treating cancer that sound as if cancer should all be cured, but it isn't, even though the principle is not incorrect.