When you say to someone that you like or dislike something and they respond with "Why?" how do you respond? I usually say "I don't need a reason."

You have a very good answer.

If I am asked why, I usually explain why. People usually say "I don't need a reason" when they can't think of a reason that would be socially acceptable.

I say, "What are you, the _____ police?"

The blank of course being whatever it was I liked or disliked. 

That will work.You forgot the "effing"

I disagree...It is truly none of their business and we don't need reasons why we like or dislike something.