Well, it appears all those alties were right, and cancer is a modern disease that was unknown in the ancient world. A paper in Nature Reviews Cancer (which is embargoed for a full year (!) for electronic access so only subscribers can access it) is reported in a University of Manchester press release. This finding is based on analysis of hundreds of Egyptian mummies, as well as reports in literature and earlier animal studies. Just exactly what was examined is unclear in the press release:
The team studied both mummified remains and literary evidence for ancient Egypt but only literary evidence for ancient Greece as there are no remains for this period, as well as medical studies of human and animal remains from earlier periods, going back to the age of the dinosaurs.
As the team moved through the ages, it was not until the 17th century that they found descriptions of operations for breast and other cancers and the first reports in scientific literature of distinctive tumours have only occurred in the past 200 years, such as scrotal cancer in chimney sweeps in 1775, nasal cancer in snuff users in 1761 and Hodgkin’s disease in 1832.
Presumably the full paper provides further information, especially since the body of literature, records, reports and papryi from early Egyptian to late nineteenth century would, presumably, be too large to examine in full. Their study gives a clear result (EoR's emphasis):
Professor Rosalie David, at the Faculty of Life Sciences, said: “In industrialised societies, cancer is second only to cardiovascular disease as a cause of death. But in ancient times, it was extremely rare. There is nothing in the natural environment that can cause cancer. So it has to be a man-made disease, down to pollution and changes to our diet and lifestyle.”
But what about those ancient cases of cancer that clearly aren't modern?
Professor David – who was invited to present her paper to UK Cancer Czar Professor Mike Richards and other oncologists at this year’s UK Association of Cancer Registries and National Cancer Intelligence Network conference – said: “Where there are cases of cancer in ancient Egyptian remains, we are not sure what caused them. They did heat their homes with fires, which gave off smoke, and temples burned incense, but sometimes illnesses are just thrown up.”
She added: “The ancient Egyptian data offers both physical and literary evidence, giving a unique opportunity to look at the diseases they had and the treatments they tried. They were the fathers of pharmacology so some treatments did work
She concluded: “Yet again extensive ancient Egyptian data, along with other data from across the millennia, has given modern society a clear message – cancer is man-made and something that we can and should address.”
Finding cancers in ancient Egypt does rather seem to dispute the conclusion that cancer is 'man[sic]-made' and a 'modern' illness, while the dismissive "sometimes illnesses are just thrown up" is simply misdirection.
New Scientist examines these claims, noting that there are multiple natural and genetic causes of cancer, that many modern cancers are a result of lifestyle choices rather than a toxic environment, and that many modern cancers are due to increased longevity.
Cancer Research UK discuss the history of cancer, noting that dinosaurs probably suffered from it, and the earliest record of tumours (in the breast) is found in an ancient Egyptian papyrus. Hippocrates also wrote about cancer.