This rotation pattern is so it all works out in the long run after several rotations. The first time you rotate tires, crossing one pair or both pairs will make almost no difference. But if you cross both now, think what happens the next time. You cross both again, and you are right back where you started!
BUT, take the front ones straight back every time, and cross the rear ones as they move to the front. Now do it again. You will see that, after the second rotation compared to the original arrangement, each tire is now on the same axle but on opposite sides from where you started. Keep this up and each tire will end up going through all four positions.