Yeah it shouldn't have snapped, good chance the rope was already cut or damaged in some way that weakened it.
I always inspected whatever length of my steel wire rope (and re-coated it with rust inhibitor) I used, every time I used it. At LEAST twice a year I unspooled the whole thing, inspected and re-coated it, then hooked it to something with some weight (usually my quad in neutral) and wound it back up.
Synthetic is nice in that it doesn't need to be coated like steel does, BUT you've got to be more careful with abrasions, and depending on the synthetic material it could 'dry rot' and weaken over time if it isn't used.
If you haven't used it much, or if you let it overlap itself and pull it out rough, it could be weakened and that could be why it snapped.