I have thought long and hard about how parent's should have equal responsibilities in their child's life. It's not up to just one parent to do everything for the kid they should split it equally. Kids are hard to keep up with sometimes and it's most definitely hard for one parent to be doing it alone while the other is around but won't play a role in raising a child. The kid will most likely grow up only listening to the parent who raised the child. In this situation it should be what is best for the kid and how your decisions affect your relationship.
In "Parent's Connect," it says that men have gotten better about taking a bigger role in the responsibilities of their children, however, it states that when both parents have a full time job the mother is still more likely to take the responsibility of the child. As a result to the women being the primary care givers they get frustrated more and will let their partner know when they are mad. This website gives you a bunch of information about good steps to take in order to equalize the responsibilities between parents. A few good steps to take are to discuss with one another about how the other feels, try and come up with a plan to share responsibilities. Obviously the responsibilities won't be equal but at least the parents can hear what each other has to say and then try and find a happy medium. Avoid negative remarks, when talking to your partner don't point fingers, suggest ways the other can change to help out more. It's good to toss around ideas to see what can and will work instead of what wouldn't work.
Bunching a few websites together I have come to see that when the child is a baby it is more cared for by the mother but once the baby turns into a child the dad steps in more because the child is now mobile and can do active things. The father needs to realize that he needs to be there even when the child is a baby, the baby grows on connections with certain people and the father should be one of them.
On a personal note, I was never really that close to my dad when I was growing up, he and my mom got a divorce when I was two years old so I was mostly raised by my mom aside from the every other weekends with my dad. When I was growing up I didn't really respect my dad all that much, I would only listen to my mom, since she was the one who raised me. But as I got older I started to respect my dad because he was more so in my life and helping me out. Now he is a big part of my life and I don't know where I would be without him. So I think it's very important to have both parent's sharing the responsibilities of raising a child.