I just saw a link in my inbox that actually says "BREATHING CAUSES CANCER"
Of course I clicked that link! How could I not! Only to find...
Lung cancer incidence decreases with elevation: evidence for oxygen as an inhaled carcinogen
Which is something totally different.
This study looked at rates of lung cancers incidence across different elevations. They found that higher elevations had less respiratory cancers. There was no association between elevation and other kinds of cancer. What this research really says is that there appears to be a connection between amount of concentration of oxygen in an environment (there is less the higher up you go) and certain respiratory cancers (lung caner).
It makes sense that oxygen would play a role in lung cancer. We use oxygen for for energy and our cells are the power plants of our bodies. When we take in oxygen it can be converted it to a reactive form which we can use to fight microbial invasion and infection. The downside being that these Reactive Oxygen Species are, well, highly reactive and can damage our own cells as well as causing mutations in our DNA.
There could be all kinds of reasons for this. ALL KINDS OF REASONS. (My first thought was, I wonder if it's hard to smoke at higher elevations? Does it feel weird? Are the effects worse? More research required!)
So ultimately, yes, we can inhale things that might stimulate the start of cancers... But breathing does not cause cancer.