You are fighting elites because the "NEW Covenant" has formed (Elites, Hunters, Jackels and grunts). Basically The Covenant break do to the prophets being fake, Elites (Sangheili) kill all the prophet race (San 'Shyuum) and the brutes basically run away out of the picture. Basically the elites don't know what to do, there whole lives as all warriors. That means no farmers, scientist, on and on. So in the end Part of the elites deside to believe in the gods and so so set out to find them (the ones you meet in Halo 4) while another group of elites led by the arbiter tries to rebuild the elite society.
While anyone can enjoy Halo, the books really build the story and add more to the game. Highly recommend grabbing a few of the halo books. You will not be disappointed.