Actually, this is exactly what gorillas do. When there is a new alpha male, he will go and systematically kill all the baby gorillas who are still nursing. Why? So he can impregnate the mothers of these gorillas who are unable to reproduce while they are nursing. While human females can get pregnant while nursing a baby, they are less fertile during the first few months of breastfeeding.
Now I'm not saying this the reason why some people have this impulse. Just thought I'd share some interesting info with you. Happy new year!
Edit: I am not an expert on gorillas, just something I have recalled from reading Robert Sapolskys book, "Behave". I'm sure there is some nuance to this infanticidal behavior of gorillas which I have misrepresented. Apologies in advance to the primatologists who read my comment.