Baby mom(s) and baby dad(dy) are relatively new. I can't put an exact origin on them but that doesn't matter. What matters is their usage.
In short, the terms are disassociation's from a parental roll and relationship to the other parent. What does that mean? It illustrates that the relation to the other parent is not a direct connection but only through the child. It lessens the other parents worth and attempts to weaken the responsibility of involvement of the two parties that created the child.
This type of thinking and behavior has two fallout's: First, it has become far too easy and trendy to have children and not be involved with their lives. Second, more and more single mothers are left to fend for their children, some times from multiple fathers, either on their own or through the help of friends and family.
The divorce rate is pretty high but the rate of unmarried single mothers is even higher. I'm not advocating that marriage is for everyone but I do believe that both parents should be actively involved in the development of their children.
Actively involved doesn't mean seeing them every few days or sending money. It's both parents making the decisions that will impact the child's life; sports & activities, schooling & child care and religion & culture as well as discipline and play. No parent should dominates in these choices alone nor should they have to.
We need to evaluate slang a little closer before we adopt it.