"It is an urban myth that people have children to get benefits"
Honestly I'm not sure that it is, or that it should carry a huge amount of blame.
The majority of women who are having babies young and outside of stable and long term relationships are very young, poorly educated, and are right at the bottom of the income distribution range, even when they work, because they tend to be over represented in the 'minimum wage, poor job security'' group.
What chance do these women ever have of a stable income and a secure home if they don't have children? They have little or no hope of social housing if they don't have children, private sector housing is expensive and wages for this group are low. The majority of men who are separated from their partners pay nothing towards the upkeep of their children, the state is a safer and more reliable provider than the majority of men in some social groups.
It makes absolute sense to me that having children in order to access housing and a stable income is something some women choose to do - most women want children anyway, and if there is a dearth of men within their social group willing and able to support a family you can see how it happens.
I'm not condemning this behaviour - it's probably what I'd do if I was in that situation. I've always wanted a family and a home, like most people, but I was lucky enough to be born into a sector of society where people earn enough to support a family, and where men are willing to marry their partners and provide for their children.
"You pay your taxes (NI) for that reason right to help others who need support and so that should you yourself need help than you will be supported."
Surely the answer is not to remove that support for everyone else, because the system of means testing is discriminating unfairly against some individuals? The answer is to look at the way means testing is working - as it's this which is resulting in unfairness to people like your mother. Calling for more means testing and tighter regulation? Why? How does that help people in your mothers situation? Or is it a case of 'if we can't have it then nobody else should either?'