Contrary to popular opinion: Poly / ENM relationships are not inherently more likely to end in messy breakups.
IMO, there are a couple reasons why this misconception exists.
More relationships = More breakups. The vast majority of relationships, including monogamous relationships, will eventually end. Nonmonogamous people have more relationships between more people; mathematically speaking, we're going to experience more breakups. This can make it look like nonmonogamous relationships break up extremely frequently, and our monogamous friends tend to read this as “messy” behavior.
Lowered expectations for longevity. Amatonormativity mandates that we view breakups as inherently negative. Relationships are expected to last forever, and if a relationship ends then it has "failed". In practicing nonmonogamy, we defy and deconstruct amatonormativity. In general, nonmonogamous folks are more likely to view the end of a relationship as a natural conclusion, while monogamous folks are more likely to cling to a relationship that’s past its expiration date - a tendency that leads to heightened tensions and increased drama. Obviously, not all monogamous people do this, and not all nonmonogamous people are good at letting go of what no longer serves them. However, the fact remains that nonmonogamous people do tend to end relationships more easily - but these endings are more likely to be amicable.
I’m sure that there are more contributing factors to this than I’ve mentioned here; I’d love to hear more from the community about your personal experiences and opinions on this. I think it’s important that we address this misconception, particularly through the lens of amatonormativity. Amatonormativity certainly affects monogamous relationships too, and everyone can benefit from unlearning the toxic belief that one singular lifelong romantic relationship should be the center of one’s universe.