in reality, you as an individual can't press charges. Only the state can. And many times the state chooses not to. You can sue in civil court, but individuals can't bring cases in criminal court.
You are confusing pressing charges and indictment. Pressing charges just means you accuse somebody of a crime and “press” the prosecutor to indict them. So the state does have the ultimate say on who is prosecuted, but that doesn’t mean you can’t press charges.