Gaius had a realisation there were terms, such as deuteragonist and tritagonist and it gave him pause for thought.
The thing is, ignoring pure character drama; most of the “how to” books I’ve looked at try to get you to be able to condense your story into a single, central, theme / struggle to achieve a single, recognisable objective. In that context, it seems logical to assume that the antagonist _must_ be very important to the story. But does that mean s/he must also be the second-most important character? For example, in Harry Potter, the antagonist is almost a bit-part! Maybe this is a trivial question as, from the top of my head, I can see no good reason why the antagonist needs to be anything more than an obviously bad “bad-guy” (at least from the POV of the protagonist). Equally, it is much easier to leave questions in the mind of the reader if you don’t allow them to see the workings of the antagonist’s mind.
So, is there ever a case for the antagonist to be treated as a major character? Surely, if the reader is exposed to both sides of the argument with equal or near-equal weight, they will find it difficult to sympathise with your hero/heroine as they could easily find the antagonist’s arguments are more convincing. (Speaking as a child of Guardian readers, I understand the perils of seeing both sides too clearly.