How does alcohol raise the risk of cancer?

Unknown: The exact mechanism by which alcohol increases the risk of cancer is unknown, but this risk is well-established for cancers of the head and neck, breast, liver, esophagus, and colon. There are probably many different causes including a local irritant effect, the effect on how other drugs are metabolized by the liver, and the effect of metabolites of alcohol that may be affected by gut bacteria.

Nobody knows really: There are a lot of theories, the main one is that alcohol is known to induce enzymes in the liver that metabolize other substances, including alcohol itself. Many substances we take in through food or even water may be metabolized into cancer-causing chemicals (like the good black stuff on barbecued skin), and alcohol causes us to make more of these. It is also a chronic irritant to tissue.