Although Dyneema is very strong, it has virtually no stretch. If subjected to a sudden shock load by arresting the fall of a weight it could fail before a similar, or theoretically weaker, sling made from nylon.

These slings are, however, popular with climbers where saving weight is crucial. In the event of a Dyneema sling arresting the fall of a climber their own body and their climbing gear will act as a shock absorber [...and I’m not saying that is a good thing]