Unfortunately, each of the three theories about how agnostids lived has a serious weakness.

First, we know that other types of arthropods swam in the open ocean, hunting their prey. However, all of those arthropods had large, well-developed eyes. Vision is one of the best ways for a predator to track its prey. But agnostids had tiny, poorly-developed eyes and were sometimes completely blind! This seems to rule out the idea that they were predators. If they did chase after prey, they would have had some other, special sensory organ to help them find prey, but there's no evidence of this in the fossil record.

Second, it seems unlikely that agnostids lived on the seafloor. Animals that are seafloor dwellers typically don't have the ability to move very fast or very far. They move slowly across the seafloor and stay in localized areas rather than spreading to new areas. So, typically we find each seafloor dweller species occupying a small geographic area where it had originated and nowhere else. However, many agnostid species inhabited multiple geographic areas spread across large distances. This suggests that agnostids were able to move from one area to another pretty fast. The ability to move easily across large distances would be highly unusual for seafloor dwellers.

Finally, the parasite theory. Well, one thing that's typical of parasites is that their populations are not very large. Parasite populations have to stay within certain limits, because if there were too many parasites, they would kill off the host organisms they live on. But we're pretty sure that the populations of many agnostids were in fact very large. We can tell because for many species we've been able to find vast amounts of fossilized individuals. So, the great size of agnostid populations seems to rule out the theory they were parasites.