Do you say you won't get mad if someone tells you something, then get angry?

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I believe that all communication should be open for relationships to work. This being said, I also believe that sometimes it is best to not tell people everything (the equivalent of being polite by not telling someone if they are fat: don't hurt people's feelings with pointing out unnecessary things). I had an opinion that I did not want to share because I felt that it would be unnecessarily hurtful, but then the person directly answered me. It put me in a moral dilemma. I knew that they would find it hurtful, but I didn't want to lie. The question was so direct that I couldn't sidestep it, so I said, "I don't want to hurt your feelings by answering that." and that made them insist that they wouldn't be hurt/angry and ask more and more direct questions until I told them. Then they got angry. What could I have done in this situation? I don't know how I could have avoided answering the question, and I can't lie to them about how I feel without feeling dishonest.