It is questionable whether smallpox is alive and so whether it can go extinct. If in some sense it can go extinct it seems both the Americans and Russians are determined to keep it alive "just in case".

Nobody was much concerned when we eradicated another infectious virus. Unlike Smallpox there was no "military rationale" for keeping copies on ice, so Rinderpest is gone. It appears that its close human relation, Measles, will be around for a long time though because "I don't believe in facts" trumps "My child has died of a preventable disease". So that's certainly evidence for you're "We're a funny lot" theory.