How does fast food cause cancer?

There is no evidence to suggest that any type of cancer is caused by fast food - or any food. The causes of cancer are not known.

A diet high in processed meat is a major risk factor for colorectal cancers; it is also a known risk factor for stomach cancer, as is a diet high in salt. A diet high in fat is thought to be a POSSIBLE risk factor for a few types of cancer; a diet high in dairy is thought to be POSSIBLE risk factor for prostate cancer. (A risk factor is not a cause).

That's pretty much it for the known or suspected links between food and the 200+ types of cancer.

Cancer is an ancient disease as old as humankind and older, so has been around much longer than fast food

since they don't know what causes it, don't know
where did you hear it did?