Leaving aside the fact that fossil fuels pollute the atmosphere and contribute to climate change, they are simply finite and so exhaustible in supply. Data from the UK Governments 2016 Fossil Fuel Price Assumptions for the UK projects over 90% increases in the cost of coal and gas by 2030, with the cost of oil more than doubling. Furthermore, the data provided is intended to reflect long-term trends in fossil fuel prices and not short-term price shocks.
For the average UK consumer, this is likely to make energy unaffordable. Sustainability is about finding an enduring solution to this problem; one that can be sustained indefinitely and preferably to the benefit of both the consumer and the environment.
Renewable energy is one such solution, and it matters because it protects you, the consumer from competition for finite resources. It does this by providing access to and ownership of abundant and clean resources, without being dependent upon third party providers.
Quite literally, sustainability is about putting the power in your hands.