If unions are not monopolies, what market structure do they fall into?

I have an example to prove my point....in a market with a monopoly (a single seller) and a monospony (a single buyer)...the only way to determine price is through collective bargaining. Why, then, do the NFL, NBA, AND MLB engage in collective bargaining? See...it makes no sense if I am not right. But, I am right...fact is..in the nfl...the player union is a monopoly, the owners are a monospony..thus the need for collective bargaining.