This refers to some addicton - probably alcoholism. An alcoholic cannot drink even one dring of alcohol. If they do, they will only want more and keep drinking as long as there is alchohol available. To become sober, they must go through a painful process of withdrawal. This is the meaning - just one drink will send them on a drinking spree, so one drink will be too much; once they take that one drink, they can never get enough until someone or something makes them stop.