Somewhat like a Mindfuck. Paradoxes are usually used as an example for the impossible or that god exists. Such as with every negative will come a positive.
If there is Anti-Matter, how can there be matter?
The girl died of , but thanks to the research done by the scientists based on her case, they were able to save the lives of many others.
You prevent your mother from creating yourself with your dad. But as a result, you wouldn't exist, therefore you couldn't do it in the first place. It's essentially an endless cycle.
These are examples of a paradox.