Voting is a major responsibility of a U.S. citizen because participation is the basis of democratic government. As Abraham Lincoln put it, democracy is, "a government of the people, by the people, and for the people."
"By the people" would not be highly acknowledged if people will not choose their desired leaders through fair elections. It is a right of every U.S. citizen to vote because they have every right to choose who should govern and how they are governed.