The paradox is the dead-alive state that the cat is in before the observation.
The paradox is designed to make quantum mechanics look absurd or equivalently show that quantum mechanics predicts an absurd world.
Some people interperet this as saying the world is strange, and some people interpret it as saying quantum mechanics is strange.
For the record, "Shrodinger's cat" originated as a throw-away line in one of Shrodinger's papers about the statistical interpretation of wave mechanics, and the writing is neutral enough, with the author suggesting the absurdity of the cat situation, and allowing the reader to draw his conclusions.