(I was scooped by Wedrifid, but here's my phrasing.)

The opposite of happiness is sadness [...] Anyone who says otherwise fails at opposites, and should probably retake the first grade.

I say otherwise. Specifically, it seems to me that the opposite of happiness is a type error; not everything has to have an opposite, and most things don't. The purest examples of what we call opposites have a duality to them, a one-dimensional-ness: it makes sense to speak of hot and cold as opposites because temperature has an order relationship to it; if the temperature is changing, it's either getting hotter or it's getting colder, but not both or neither. Similar remarks could be made about left and right, or the boolean values true and false. But most useful concepts are way too complicated for this kind of duality to apply: what's the opposite of blogging? What's the opposite of graphite? What's the opposite of Vernor Vinge? These questions simply have no sensible answer.

Oftentimes we like to contrast two different things, but this should really be kept conceptually distinct from those things being opposites. I would expect your star first grader, when queried about the opposite of cat, to unhesitatingly reply, "Dog!" (I haven't actually run this experiment, but in any case I certainly wouldn't expect her to say, "Your question is confused; I cannot answer it as stated.") I share the intuitions that make this response seem compelling, but from the standpoint of understanding reality, it's laughably, egregiously wrong. Cats and dogs are just two species that happen to have been domesticated by humans and commonly kept as pets in certain cultures; if people in those cultures have made a habit of contrasting them, it's a historical accident of no inherent significance whatsoever.

Some might readily concede this point with respect to such non-opposites as cats and dogs or salt and pepper, but object that happiness and sadness are different. And, to be fair, it is true that if we were to metaphorically project the configuration space of human emotions onto the one-dimensional subspace measuring the extent to which humans will try to seek or avoid those feelings, then, yes, happiness and sadness would be on opposite ends of that line. But they're still ultimately just these different massively complicated, historically contingent (on an evolutionary timescale) neurological phenomena. Other humans will know what you mean if you call them "opposites," but that doesn't mean it actually makes sense to do so.