The national center for men argues that it is fighting for "fairness and equal rights." the center feels that divorce laws in particular put men at a disadvantage, forcing them to pay more than their fair share and denying them access to their children. what kind of a group is the national center for men?

The answer to this question is part of the men’s rights movement
The men rights movement believe that since the past decades has solely been focused solely to fix women's right, now the balance within the society has been tilted to their disadvantage. For example, they believe since the majority of household income is contributed by the male counterpart, it is unfair to split it 50-50 in the time of divorce.

The answer is price.