The fathers' rights movement is important not because it benefits men, but because it benefits children. Shared parenting is extremely important for the health and well-being of children vs having a single mother as their primary parent and an estranged father that the children only get to spend time with a little bit out of the year.
Brushing off the importance for children to have equal involvement with their father by saying something to the effect of "oh, men have had better rights in other areas so having little to no rights when it comes to parenting is justified" only serves to hurt children in the long run.