A German compound noun meaning "an intense dislike and disregard for children" according to Florence King in her book The Florence King Reader." The only online German-English dictionary that seemed to contain it only had the expression "kinderfeindlich sein," translated as "to hate children." (In German, "-keit" changes an adjective into a noun, like "ness" or "osity" in English.)

There is something to add to Segnbora-t's wu.
Kindefeindlichkeit is a noun usually used in context of social groups or the society altogether.
It means that in the social group/society having and growing up children is discouraged, mostly by hampering and discriminating people with children. I hasn't to mean that children are directly disliked - it's more like It's good to see that someone has children here. Please make sure that they don't make noise, expect perhaps 9-10 am and 3-4 pm, thanks.
It's rarely used in the context of individuals, then it would really mean hating children, and it's rather offensive.

And, of course, why exists this term ?

Deutschland ist kinderfeindlich !

This is true, in fact.