If answer A would be correct, then answer B ("Answer A or B") would also be correct.
If answer B would be correct, then answer C ("Answer B or C") would also be correct.
This leads to the conclusion that if either answer A or answer B would be the correct answer, there are at least two correct answers.
This contradicts with the statement that "there is only one correct answer to this question".
If answer C would be correct, then there are no contradictions.