The government intends to cut Child Benefit by suspending payments to families where one person falls into the higher tax bracket. There are two main objections to that proposal. One is that it is inequitable: it allows households on higher incomes to retain the benefit while cutting it to some people on lower incomes. The second is that it is impractical; there is no easy way of identifying who should be affected.
The main argument for cutting Child Benefit seems to be that it will help to cut the deficit. If the government wanted to increase the burden on richer families, it has the option of clawing back the benefit through the tax system. It would make more sense to tax all higher rate payers, rather than only those with children. If the government was serious about cutting the deficit, they would be raising tax. The fact they are not talking about raising tax is a strong indication that this is not really about balancing the books. They are focusing on public spending, which is quite a different issue.