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 agnostids 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 that they were parasites.
The professor in the listening part thinks the theories in the reading passage do have some weakness.
First, the agnostids could hardly be a free-swimming predators. Nowadays, open sea predators always have well-developed eyes in order to chase and caught preys. However, accord to the fossil discoveries, the agnostids don't have related high developed organ providing them with nice vision. In other words, the agnostids' eyes are really poorly developed and possibly blind. So, it is unlikely they can get food like a free swimming predators.
Second, the agnostids usually can be found at multiple places. This means the agnostids is unlikely a seafloor dwellers, which move very slow and always stay at one area of the sea floor. The agnostids constantly spread to diverse places which means they can move pretty fast. So, the agnostids is not a seafloor dweller as the reading suggest.
Third, the agnostids can be found at one place where there are many of them. While for a parasites, they usual not so crowded at one place. Because too many of them can cause the animal they are feed on died. And the fossils find many individual agnostsids, which not support the they are actually parasites.