The current setup is far more progressive than 'free' tuition fees.
Under the current system, if someone goes to university - thereby upping their earning potential - and earns enough to pay them back, they do so slowly over a number of years. If they don't end up earning enough to pay them back, they don't.
Effectively tuition fees function as a means-tested tax on having a degree.
In contrast, providing free university tuition means students' degrees are subsidised by all taxpayers in the country including those taxpayers without the academic ability to benefit from university education themselves. Effectively it takes money from the entire tax base, including the poor / undereducated, to improve the life chances of people who already have more academic ability and hence better chances. How is that fair?
You only have to look at what's happening in Scotland to see the reality of 'free' university tuition: 'free' places are sharply restricted while universities shill like mad for paying students from England and overseas so as to make up the shortfall in funding.
It might seem counterintuitive but your Tory voting mother is supporting an education policy that delivers a far more socially just outcome than taking tax money from bus drivers, road sweepers and plumbers to fund someone else getting an earnings boost from university and graduating debt-free.