Do you have a link to the video? I'm wondering if you have caught the pattern of emphasis correctly. I'm wondering if the context could have been something like this: "These tiny copepods live by eating the algae they swim among. So do some of the largest animals. Only, the largest animals _dive_ for _their_ algae." In other words, "only" is a linking word meaning "the same in one way, but different in another way," rather than meaning "this is something that is only possible for the largest animals."

I don't think this is a language question, but a biology one. Clearly you understand that large animals dive and small animals don't, but the why can only be answered in context of the video, which is not a linguistic issue.