If it's your moral position to avoid animal products, so be it, but don't think you're doing it to improve your health.
Did you read it far enough to get to the part about correlating foods with cancer risk?
If you did, you are implicitly saying that broad-based search for significance on survey-based data sets is good enough science to plan your entire lifestyle around it.
Many people saying similar things does not make any of them correct. Being correct makes them correct. And to be correct, we have a religious ritual known as the scientific method, wherein the value of your conclusion is dependent not only on the strength of your data, but also how you collected it, and even how you asked the question that you wanted to answer.
According to the article, the overwhelming majority of dietary studies do not strictly adhere to the ritual, and therefore produce unreliable results. So if you would, please indicate the biochemical mechanism by which ingested meats promote any single type of cancer.
When you say "saturated fat", "trans fat", and "animal cholesterol", you are eliding over the fact that these are not specific chemicals, but broad classes of many different chemicals, each of which has a distinct biochemical role in humans.
For instance, the trans fats in meats and dairy are, specifically, vaccenic acid (18:1 trans-11) and rumenic acid (18:2 cis-9 trans-11), along with a few other conjugated linoleic acids. They are produced by gut bacteria. There's a fun article about those, showing how rumenic acid is actually the trans fat that prevents breast cancer in rats, by interrupting the normal conversion of VA to RA. [0].
The trans fats in partially hydrogenated oils are an entire zoo of chemicals, most of which are not naturally produced by the intestinal flora of livestock animals.
And stearic acid (18:0) and lauric acid (12:0) are probably healthier in isolation than palmitic acid (16:0) and myristic acid (14:0). Meats, while having a higher saturated fat fraction than vegetable oils, also have more stearic acid in proportion to palmitic.
Additionally, humans can and will convert stearic acid (18:0) to oleic acid (18:1 cis-9) with stearoyl-CoA 9-desaturase, and palmitic (16:0) converts to palmitoleic acid (16:1 cis-9) by the same enzyme.
So what chemical present in all meat promotes the cancers?
Scroll down to references and citations, and educate yourself about the trans fats that are present in meat and dairy.
You may wish to re-examine your previous claim that vaccinic acid and conjugated linoleic acids may contribute to negative health effects when eaten with meat.
It is also worth mentioning that some of those trans fatty acids are produced by bacteria found inside the human intestinal tract [0]. You're getting those anyway, whether you eat meat or not.
Can you identify one or more of the saturated fats found in meat that produce adverse health effects? Better yet, can you identify the reactions in the biochemical pathway that produce those effects?
I am reluctant to accept your apparent claim that "saturated fat is bad for you", when I am well aware that medium chain saturated fats are sent directly to the liver, whereas long chain saturated fats are assembled into triglycerides if not already in that form, packaged up with cholesterol and protein, and transported through the lymphatic system before reaching the bloodstream.
As the original article stated, correlation based on survey responses is a weak, weak, weak way to do research.
It may be true that eating meat is relatively unhealthy. But it also may be the case that the unhealthful effects are produced by the Maillard reaction products from the cooking process, and that changing the preparation method removes the additional health risks [1]. You won't know until doing enough real, rigorously scientific studies to more precisely identify the mechanisms in play.
[0] http://www.ncbi.nlm.nih.gov/pubmed/19118369
[1] Some raw meat advocates already believe this.
http://nutritionfacts.org/video/the-saturated-fat-studies-se...
http://nutritionfacts.org/video/the-saturated-fat-studies-bu...
http://nutritionfacts.org/video/trans-fat-saturated-fat-and-...
In the last 30 years there have been studies claiming that with very very good methodology, you could cite some of the stuff from the '80s and you wouldn't be incorrect.