An office printer had an option for automatic duplex printing, but not manual. So I had to command it to print firstly all even pages in normal order, and they ended at the paper output tray face-down (p. 2 was at the bottom).
Then I turned them upside down, and placed them back into the paper feeder tray, so that p. 2 now faced up and was the topmost sheet. I printed all odd pages in normal order. At the paper output tray, the most bottom sheet contains p. 2 (facing down), p. 1 (facing up; reverse of p. 2). The second most bottom sheet contains p. 4 (facing down), p. 3 (facing up; reverse of p. 4). So the front-to-back order is wrong, as it's p. 2, p. 1, p. 4, p. 3.
How can I manipulate this printer to flip pages horizontally, rather than wasting my time flipping manually? Yes, I was foolish not to research first and read this.