Hi TJ!
There's something weird about how toxicology of carcinogens is determined. Let's see if I can explain it. For MOST toxic substances (that would cause the liver to die, for example), there is a "safe dose" and a dose that is unsafe. Below a certain level, and your liver will always be fine. Above a certain level, the liver always dies. This isn't quite accurate for carcinogens because of the way they work. Carcinogens often work by causing mutations, and mutations are a matter of exposure + bad luck. Therefore, in theory, if you're the unlucky one, a single molecule of a carcinogen can give you cancer. This is why sometimes you see people that "never smoked, never drank" yet got lung cancer anyway. However, repeated exposures to carcinogens certainly do increase your risk of cancer - roll the dice again, and you'll eventually get snake-eyes. And some carcinogens are worse than others. It's tough to see this reported, because even the barely carcinogenic stuff has no theoretical "safe dose" because someone could have really bad luck.
I don't know how that may have influenced the list.
I do know a bit about why meat is so bad. You'll want to cut down on the meat, honestly - maybe not completely eliminate it, but the way it is consumed in the standard american diet increases people's cancer risk by a number of mechanisms. Here they are:
1) Deli meats are kept preserved with nitrates. Those are potent carcinogens.
2) Smoking and grilling produces pyrenes. These are potent carcinogens, similar to the ones in cigarettes.
3) Frying meat produces acrylamides (really, frying anything produces acrylamides, meat is worst)
4) Even if you just "bake" your meat, you're still not safe. Eating a lot of meat makes food get stuck for a long time in your colon and rectum. Partly digested food sitting around is not good for your back end. Meat eating is well known to increase the risk of colorectal cancer.