Pressing can help your team gain both an offensive and defensive advantage. These are instances when you'd want to press: The opponent has poor ball-handling ability. A poor ball handler is anyone who makes turnovers.
Your point guard O1 can pass to the middle, or to O3 or O5 in the corners. In fact, most half court presses are vulnerable down low in the corners. Good accurate long passes over the defense into the corners will often beat this defense. If the back defender starts cheating toward the corner, then the middle is open.