Why do we think chronic inflammation can cause cancer?
There are good epidemiological data for this.

Links between cancer and inflammation were first made in the
nineteenth century, on the basis of observations that tumours often
arose at sites of chronic inflammation and that inflammatory cells
were present in biopsied samples from tumours.
There are many triggers of chronic inflammation that increase the risk
of developing cancer. Such triggers include microbial infections (for
example, infection with Helicobacter pylori is associated with gastric
cancer and gastric mucosal lymphoma), autoimmune diseases (for
example, inflammatory bowel disease is associated with colon cancer)
and inflammatory conditions of unknown origin (for example,
prostatitis is associated with prostate cancer). Accordingly,
treatment with non-steroidal anti-inflammatory agents decreases the
incidence of, and the mortality that results from, several tumour
types.

Cited from Mantovani, Alberto, et al. &quot;Cancer-related inflammation.&quot; Nature 454.7203 (2008): 436-444.
http://www.sld.cu/sitios/reumatologia/temas.php?idv=21500