Stop thinking about pressing the bar away from you. Think about pressing yourself into the bench. Imagine for a second that the barbell was stationary (it wasn't going to move), but the bench underneath you did move. You're trying to push yourself into the bench, and what that prevents is reaching. A lot of people will bench and they'll kind of lock out... where they're reaching to finish that last rep and they lose all upper back
tightness. Then they're left trying to find it, digging around on the bench.