He's basically telling his daughter that in his opinion she is not an adult, not ready for this. If she wants to disagree, then she is saying that she is an adult. For a daughter to say, "I'm an adult and I can do what I want ... oh by the way, could you buy some diapers and formula when you go to the store?" is trying to have it both ways.
My daughter is still at least a decade away from this becoming an issue, so I can't swear to how I will feel when it is. But I do believe there are times that parents should tell their children that they (the parents) will not support certain decisions. Having a child is a special case, in that the decision can't be changed so there is no chance to reconsider.