We are a pretty selfish species and every one of us are inclined to think OUR STUFF is the most important. "How am I going to take care of me and mine", becomes a primary concern. "Enough about me, what do YOU think of me?"
So let's face this part honestly: regardless of what happens to any one of us (or ALL of us), the Earth will still spin on its axis and the Sun will rise tomorrow.
To realize that though, one would have to know that the Earth does, in fact, spin.
In order to really grasp astronomical issues, we first need an understanding of terrestrial problems; the less selfish of us may ask yourself the "bigger picture" questions:
All this baggage can really start to bum a brother out.
So, as human beings, we have things we have to do to stay alive and live a quality existence, both for ourselves and each other.
This is where knowing about astronomy comes in and why it matters.
You have a responsibility to others to make good decisions in an attempt to contribute to the betterment of all, or to at the very least, not make things worse.
To do that, you need to know things.
To live the fullest, most enjoyable life possible, you must understand it.
So yes, the problems down here on Earth matter, but solutions to them require context that only a knowledge of planets, stars and the universe as a whole can provide.
Knowing and understanding the stage on which your life is being played is crucial for any existence to have real meaning.
I mean, who the heck wants to just go through the motions? We need more than just sustenence and safety. We need quality. We need happiness. We need to know. We need to be better than when we started.
That's why we went to the Moon, that's why we built the Hubble Space Telescope, that's why we're building the James Webb Space Telescope.
So from my perspective, the question is not "Why does knowing about astronomy matter?", its more "How does knowing about it NOT matter?" or "How can you possibly live your life happily NOT knowing about it?"
Keep Looking Up!
(borrowed from Deep Astronomy)