In this work we study a simple contagion model for drinking behavior evolution, but including the presence of inflexible or zealot agents, i.e., individuals that never change their behavior (never drink or always drink a lot). We analyze the impact of such special agents in the evolution of drinking behavior in the population. Our analytical and numerical results indicate that the presence of only one class of inflexible agents destroys one of the two possible absorbing phases that are observed in the model without such inflexibles. In the presence of the both kinds of inflexible agents simultaneously, there are no absorbing states anymore. Since absorbing states are collective macroscopic states with the presence of only one kind of individuals in the population, we argue that the inclusion of inflexible agents in the population makes the model more realistic. Furthermore, the presence of inflexible agents are similar to the introduction of quenched disorder in the model, and here we observe the suppression of a nonequilibrium phase transition to absorbing states, which had not been reported before.