Alcohol is a well-established human carcinogen. Major public-health and cancer authorities state that drinking alcohol causally increases the risk of several cancers, including breast, colorectal, liver, esophageal, and head-and-neck cancers. The claim is broad, but the omitted nuance does not alter the central fact that alcohol consumption causes cancer in humans.
Caveats
This is probabilistic causation: alcohol increases cancer risk; it does not mean every drinker will develop cancer.
The strongest evidence is for several specific cancer types, not for every cancer indiscriminately.
Risk generally rises with greater consumption, and some risks are amplified by co-exposures such as tobacco.