It's a difference of state laws. You hear the term right to work state. What that means is if you are hired into a job where a union is present, you are not obligated to join that union. You can choose to work outside of that union and maintain your job. According to Wikipedia there are 23 states that are classified as right to work, most of them are located in the south. These states have very little unionization.
In the other 27 states if you are hired into a union environment you are obligated to join the union if one exists. Typically you have to work anywhere from 30-90 days as a probationary employee and you aren't officially part of the union but after that, you are a full due paying member whether you like it or not. Once a union is formed it's very difficult to remove it from the work place. The company has 2 options, fire everyone and start new. As Lee pointed out, that's not the best way to go. Or you sit and wait for another union challenge. Say for example, the Teamsters is the current union. Employees are unhappy with the teamsters and want to make a change to the AFL-CIO. In this scenario the company can step in and ask that there be no union representation. The bargaining unit would then hold a vote for A. Retain the Teamsters, B. Remove the Teamsters and go with the AFL-CIO or C. Remove the Teamsters and go non-union.