(These are all my own personal opinions - I'm not going to attempt to dissuade anyone of their own entrenched positions)
1) Inherently, all children live in poverty. The only things that they have in life are those provided for them by their parents or care-givers. The common use of the phrase "Child Poverty" is merely an effort to dress up the word "Poverty" in an even more emotive manner. The root of the problem in question is that the parents either cannot (through "Poverty") or do not (through "Neglect") provide adequately for their children.
2) "Child Poverty" is much better suited to describing situations of neglect. Where the child is deprived of love, attention, encouragement, support, engagement, etc. rather than being deprived of food, clothing, etc. I.e. it's being deprived of a loving, caring, nurturing environment to grow in - a failure of parenting if you will, rather than being deprived of material things. (which is covered more than adequately by the generic term "poverty".) In this context, child poverty can (and does) occur amongst the very wealthy as well.
3) Children are expensive. Irrespective of how wealthy a family is, having a(nother) child will always make them financially worse off.
4) (Where it gets contentious...) Families living in poverty that continue to have children are being extremely selfish.