Is it a big deal if my 11-year old daughter refused to share a piece of her favorite candy?

Oh! Yes. Once in a while is fine. She is 11, and it happens with people of any age. I remember my aunt used to hide her favourite sweet and would reluctantly share it with kids. I am not endorsing the habit, all I meant is it is just human nature. It was her favourite and it answers as why she didn't want to. Relax, and if it is repeatedly happening then explain her that even if by sharing the candy finishes, you can always get a new one for her. And that everyone has something that is favourite to them and if all go by your way, then others too would not share anything with you.

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If its once in a while then its okay, but if its a habit then she needs to be talked to. An 11-year-old is grown up enough to understand about sharing. Let her behave like a "baby" once in a while though!