I think you've missed the point though. They aren't their opposite. They are what DEFINES their opposite. It's similar to light and shadow. Darkness is the absence of light and it's shaped and defined by light. The difference with the Endless is that their opposites are quite a bit more complex than simply being the "absence of", but I think my brain would explode if I tried to really figure out how it works. Anyways the in-book example was a two sided coin. The endless are one side of the coin and their opposite is that other side. You can't have one separate from the other. It's all one thing. Despair might never actively deal with hope, but hope exists where despair isn't, so you can't possibly disconnect the two.
Also I think Death mentioned who everyone's possible opposites were. I can't recall them for certain. I always figured Desire's opposite was Hate, and it's not hard to imagine those being linked. It might have been satisfaction though...can't recall. Anyways it was something like Destiny/Freedom, Death/Life, Dream/Reality, Destruction/Creation, Desire/Hate, Despair/Hope, Delirium/Sanity.