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You were doing nothing wrong. You treated the non-believer with a spirit of gentleness, and he/she had no right to treat you the way he/she did. Some non-believers are very open to the possibility of accepting Jesus as their Lord and Savior, because they can sense that they have a hole in their hearts that only God can fill.
Unfortunately, you ran into the "My way is better than your way. You're a bigot and I'm open-minded, even though I don't want to give you the opportunity to speak your mind" kind of non-believer.
You did your best. Now, it's time to kick the dust off of your feet and move on. But never forget to pray for this person's salvation as you walk away.