Someone who is a much better historian of the English language than myself could tell when the word disposable got its current meaning, which is curiously unrelated to the term it seems to antonymize.
"Posable" as a word is much less used than its antonym, disposable. The only specific time I can think of it being used is to describe action figures, which can be put into different positions. To follow the logic of language, "disposable" should be something that's pose can be broken down. However, disposable means "something that can be thrown away".
However, a closer look at what "pose" means might shed some light on this. Pose means, in common language, a structure. Its root Latin meaning is "to place". In other words, something that is posed or posable is something that has both a structure and a place where it belongs. Something that is disposable is something that can be thrown away because both its structure and its position are contingent, it does not truly possess either. And that is how "disposable", meaning "something without intrinsic structure or position" becomes "something that we can throw away" or more simply, "garbage".