This is another one of my pet peeves, and it has bothered me for so long that I often forget to include it on the list. Still, I think it may be the most important because it does so much damage to the fight itself, not just to the individual fighter.
I know we can all agree on two things. First, a boxing ring is a square. Second, you don't want to get trapped in corners or on the ropes. Fair enough? Now if you and a rival begin, squared up in center ring and you move laterally ("side-to-side") to the right, what happens? Two things. You move yourself out of punching range and you hit the ropes. This is why you circle, not move laterally.
You can circle with a tight arc, in order to maintain punching distance while still avoiding the punches of your foe. You can make a larger circle to keep out of range, but still be only a slight move away from landing your own punches. This is moving in and out. If you watch Trinidad, especially the Barnes and Carr fights you will see this, how he tightens the circle. Same with Ricardo Lopez. The old-timers, older than me even, referred to the ring as the squared circle, and boxers like Archie Moore, Charly Burly and Billy Conn spoke about how controlling the circle meant controlling the fight.