Why should I avoid loops when designing relationships for a database?
Solution 1:
There's a really good treatment of relationship loops in chapter 3 of this paper (archive.org).
Generally however, the most common issue with loops is consistency of redundant information.
Consider the case (from the paper) where a parent has many children; each child attends a school. There is a third relationship between parent & school ('parent has child at school'). However: you don't want to model the 3rd relationships explicitly; it's completely derivable from the other two. If you did capture it explicitly, you'd need to ensure the loop was always consistent.
So in that case you'd want to avoid the loop. However: loops are not universally bad. Taking the above example again, consider modelling the case where a parent is a governor at a school. That would also create a loop. In this case though it's valid: it's not possible to derive the 'parent is governor at school' relationship from the other two relationships.
So in summary: don't model loops when one relationship is completely derivable from the others combined. But it's OK to create loops when they're not derivable.
Would recommend the paper though; it gives a much better description than I can give here.