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Oh, that's an easy question.
What's a paradox? In science, it's “a statement that, despite apparently sound reasoning from true premises, leads to an apparently self-contradictory or logically unacceptable conclusion.” (cf. Paradox - Wikipedia). Which means that such a paradox exists only so long as you don't understand it, or don't invalidate it. And when you understand each and every one of them, you realize suddenly that … paradoxes don't exist!
You just had the temporary illusion of their existence, because of either a flaw in the way it's presented, either a flaw in your default understanding mode, which we usually call “intuition”. Here is a list of some popular ones:
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Another kind of paradox is “in common usage, the word "paradox" often refers to statements that may be both true and false”. In that case there is nothing to understand or invalidate, so it's not a paradox at all from the beginning.
