A firm in a purely competitive labor market is a wage taker because

employees don't accept the wage if the firm goes for lower wages.

Explanation:

A purely competitive labor market means that employees have more bargaining power in the employer-employee relationship. They usually wouldn't settle for the wage initially offered by employers, which is mostly low at the start. They gave the impact to influence the wage, due to the labor market structure (high need for labor, or decreased number of competitive employees). Therefore, the firms in that kind of labor market are wage takers.