According to the Cambridge dictionary,
Counterintuitive: Something that is counter-intuitive does not happen in the way you would expect it to
Contradiction: a fact or statement that is the opposite of what someone has said or that is so different from another fact or statement that one of them must be wrong
How something was counterintuitive? Someone must have read or proved facts in the past and that is why one will not expect opposite things to happen in future.
If both the words are providing a sense of opposition, then what is the exact difference between them?
Also, what are the appropriate contexts to use them?