If it's moving side to side slightly, it either was always that way due to manufacturing tolerances as Dabac explained or the support arms got bent long th way by a crash or other impact, but not from simply riding.

But, as I suspect, you mean the radial distance to the cage varies, there are a number of possibilities to explain variation in the 1-3mm range.

1- you might be seeing the shorter teeth that are part of the shift gates (my term) which are intended to make shifting easier. There are usually a pair on the outer ring.
2- the same manufacturing tolerances as above.
3- if your rings are mounted supported by the bolts and do not have a supporting shoulder on the arms, they can shift slightly causing them to be eccentric. This is often an issue on single speed bikes and can be corrected by loosening the bolts slightly and tapping the highest spot toward center. This is a bit of a trial error method, and will take some time to get the ring centered well. It's useful for single speed, but you needn't bother on a derailleur bike because the eccentricity doesn't make a difference.

If the variation is much more than a few millimeters, then you probably have BioPace or some other ovalized rings as suggested above.