"there should not be a financial incentive to have children .Obviosly this would not be a retrospective action but one designed to make people think twice about bringing children into the world when they have no means to support them financially."
The fundamental flaw about this proposition: for whose benefit is child benefit? The key is in the name - it is to benefit the child. This proposal would penalise the children; that cannot, by anyone's morals (well, almost anyone's morals) be right.
Quite aside from that, I'm not actually sure why we want to be stopping people from having more than two children. Is it on an environmental basis? I can see that argument - but there's no indication that that's what this petitioner is worried about. She seems to think that child benefit constitutes a financial incentive to have a child; Her Majesty's Revenue and Customs give the lie to that theory. For the eldest child, parents get £17.45 per week, or £17.55 if for a lone parent; for each additional child, £11.70 per week. That's a very maximum of £912.50 for a child ... I don't think, somehow, that anyone who can do basic arithmetic is going to have a child because the child benefit is going to make them financially better off.