Do you have a source on that, or do you think lawmakers might also be concerned with the well being of children, mums, dads, single parents, young parents–no matter how many children/parents there are?
There are various (english) news articles (for example [0][1]) and also a paper for the European commision [2] (so called ESPN Flash Report) claiming that.
But besides those sources there is also the fact that the child-raising benefits are only unconditional from the second child on, for the first child there is a maximum monthly income to get it.[2] If the main goal was the well being part, then this would not make much sense.