I think there was quite a long debate about this on Mumsnet when it was first announced -a year or two ago. It was in the News section, I think, if you want to search.
We all make choices about whether we can have children, whether we can afford to support them, whether we can afford to stay at home or whether it is better to work or study (possibly slightly neglect our children in the short term and/or have them doing long hours in childcare) in order to provide a better future for them and ourselves. These choices are often harder for single parents because we are usually in a situation that we did not plan for and we just have to deal with it, trying to make sure that our children have the same opportunities as those in two-parent families.
The system currently makes allowances for this: Single parents only having to work 16 hours a week to claim working tax credit. Being able to claim income support indefinitely without being made to look for work. These concessions are not available to people living together as a couple. The government is adjusting and tightening up on these concessions. (These concessions are not a right. It is not that many years ago that none of these existed. Hence part of the reason that people traditionally looked down upon and pitied single mothers and saw them as charity cases.)
I don't think it is unfair as such to change things but the problem is that there is not enough flexibility in the system to cater for different individuals' situations. Working when you have one child is reasonable. Working when you have, say, three children of different ages, at different schools, or if one or more has special needs - it all starts to get more and more impractical and unrealistic, although some manage to do it. It also depends a lot on how much family support and back up you've got. And/or how much you earn and how much paid help you can afford. A single parent with loads of family backup might be better off, practically, than a two-parent family with no backup.
I think someone was also arguing in the previous debate that sometimes older children need more support than younger ones, because they might have loads of homework or emotional problems or loads of after-school clubs to go to which require lifts to and from. I suppose that last point is more about the luxury (rather than necessity) of after-school activities but you can see what they mean. So it is hard to pick an age after which all children are more self-sufficient. It depends on a lot of factors.
Of course, two parent families have some of the same problems, if both parents are working, so the debate can become mired in comparing individual circumstances. But I think this is the point. Many people, single parent and/or two parent families on low incomes, struggle. Sadly, it is impossible for the system to take into account all the individual circumstances (it would turn into another CSA) so a seemingly arbitrary cutting off point is decided upon.