It's in your own best interest
People tend to think of sustainability as entirely environmental – something big and vague, 'out there' and largely beyond their control. Catch phrases like 'Think Globally, Act Locally' only serve to reinforce the perception of sustainability as a public good to be realized only by incurring private costs. Moreover, the scale of the problem, coupled with the moral imperative to do better, inevitably provokes anxiety when you fail to live up to the task. This understanding of sustainability is problematic for several reasons, the consequence being that people often do not realize how they themselves can act sustainably, nor why they should.
For one, sustainability is not strictly an environmental issue. While the term no doubt arose out of mounting concerns about pollution, population growth and resource depletion in the 1960s and 1970s, it did so mainly in connection with finding a better balance between economic growth, increasing living standards, and ensuring that development could continue into the future, unabated by environmental limits. In other words, sustainability is not about preventing progress but rather protecting it - from itself. Striking the right balance between improvement and the status quo is, in most circumstances, a matter of personal judgement, not something imposed from outside.
Second, focusing too much on the 'global' makes the entire project seem unattainable to the average person – what difference can one person make when the entire world seems to be moving in a different direction? Even if you want to make a difference for the better, the choices and actions required to do so may seem unnecessarily onerous if you expect them to be only a drop in the bucket. Fortunately, choosing the more sustainable option is in many cases the better choice individually - it just matters how long-term a perspective you take. While the global/local connection is certainly relevant, it too often disempowers the individual. Thinking temporally, however, has the opposite effect.
Lastly, pursuing sustainability should not produce anxiety if you find yourself failing to achieve it. Struggling with the most sustainable choice is not a zero-sum game – the right course of action will vary according to the individual, to the means you have at your disposal, and to the distance into the future with which you opt to concern yourself. Going too far beyond what you are comfortable with is actually the more unsustainable course of action - being realistic about sustainability is every bit as important as is the ideal of it. The question is, where do you draw the line between what is realistic to do about the future and what is not?
So what is sustainability and why should you care? Basically, its a choice – not about how much personal autonomy to cede in the interest of global sustainability, but rather how much control you wish to take over your own future. It is about striking the right balance between building a castle to stand the test of time and maintaining a home to raise a family in. It is about realizing the local benefits that accrue from acting with an eye toward the long-term. Above all, sustainability is about being realistic about what you can do in the interest of realizing it. You should care because it's your choice to make.