Although, for the sake of arguement, in other areas of the law, all children of a person are treated equally and birth order is irrelevant in regards to the CHILDREN'S rights. For example, in estate law, each subsequent child DOES, by law, reduce the size of the "pie" that they all are entitled to split if a parent dies intestate. They are required to be treated equally financially. Not, say, 30% to the first child, and progressively smaller percentages to a child based on their birth order. The problem with the "you shouldn't have more" argument is that it is the child who is considered entitled to support by their parent. And the child has no say in being born first, or last.
All children of a father should be entitled to somewhat equivilant support by that father. In intact families, the amount of money spent on a firstborn often IS indeed reduced as other children join the family and more evenly spread amoung later born siblings. I was a firstborn, I remember there being less discretionary spending on myself when younger sibs came along.