If "answer" means a response to a question:
* Question: This is the most direct opposite.
* Silence: This implies refusing to respond.
* Refusal: This is a more formal way of saying someone won't answer.
* Evasion: This suggests avoiding a direct answer.
If "answer" means a solution to a problem:
* Problem: This is the direct opposite.
* Failure: This implies that the answer didn't solve the problem.
* Mistake: This implies the answer was incorrect.
If "answer" means a response to a challenge:
* Challenge: This is the direct opposite.
* Defeat: This implies that the answer failed to meet the challenge.
* Submission: This implies yielding to the challenge.
Other possible antonyms:
* Ignore: This means to completely disregard the question or challenge.
* Disregard: This is similar to ignore, but with more emphasis on the lack of importance given to the answer.
The best antonym for "answer" depends on the specific context in which the word is used.