Runner on third, where to you throw?

I played baseball as a kid and sometimes watch baseball but I don't understand this part of the game. It there is a runner on third and a batter hits the ball, why do the fielders always throw to first rather than protect home plate from the third-base runner??? I have seen a number of times a third-base runner score a run because the fielders have thrown to first to get the batter out and it makes no sense to me. Is there a rule I am unaware of or what?