The problem with "processed" meats is sodium nitrate...the substance used to preserve them so that they don't spoil before they're shipped out and marketed.
When heated during cooking, sodium nitrate changes into sodium nitrite, a known carcinogen.
Even without these preservatives, animal fat content alone has been "linked" to the incidence of cancers, including bowel, breast, & prostate.
Whether or not these "linkages" are in fact solid proof of carcinogenisis as a result of their consumption remains questionable, because the innumerable cancer-causing substances to which we are daily exposed are never "factored in" to these studies.
Consider this:
We in the Western world are frequently shown photographs of people in Africa and elsewhere literally dying of starvation.
Would these unfortunates feel "more fortunate" in knowing that they at least were not going to risk certain cancers later in life because they ate meat?
Of course not.
They would all think that we in the West were truly blessed to be able to nourish our bodies and to live long enough to reach the age at which we might be at risk for degenerative diseases such as cancer.
As others have already posted, "moderation" and "common sense" should serve as dietary guideposts.
*Do some research on Google, and you will quickly find that the increased incidence of thyroid cancer in the U.S.A. today, is in direct proportion to the quantities of milk consumed by children following the atmospheric nuclear detonations in the late 1940's and 1950's, done by our military to test and perfect our nuclear weapon stockpiles.
*Highly poisonous radioactive fallout such as strontium 90, carried by wind, blanketed the country, and was absorbed from soil by grass and other feedstuffs, fed to livestock, and transferred directly into their milk, which children were encouraged to drink each day.
*Nuclear test fallout, "conveniently" left out of dietetic research, is also directly linked to the increased incidence of breast and prostate cancers seen today.
*Tobacco also has been proven to include several radioactive products which may be the actual triggers for cancers found in those using tobacco products over a long period.
The sad fact of the matter is that the many benefits we take for granted in modern civilization also have their downside with regards to health risks.