Well I don't like the way it's used as a put down, and i have never said it myself (either in RL or on here) except about myself 
But there is often a serious point behind it which is that for some people their child becomes a kind of megalomaniacal obsession, totally over-riding any consideration for other adults or children.
For eg I think we've probably all been on holiday with a family who insist that all activities are done at the times that suit their baby's nap time, completely uninterested in the fact that the other families have children and babies too who also need to eat, sleep and play.
Or the parents who sit and watch their child bashing yours over the head with a fire-engine, and then intervene indignantly when you gently remove the toy.
Your child is in some ways an extension of you and it's important to have perspective and consideration about their needs, just as you would about your own..
Of course your child is the most precious thing in the world to you (be it first, last or middle born!)
But I think the overwhelming shock of having a baby can cause some parents to leave their manners and sanity at the door of the hospital - temporarily at least - and it's deeply irritating when you're on the receiving end.