What does it mean "YOUR SHAME IS TO HAVE SHAME"?

Answer 1

That is a quote from "Fish Cheeks" by Amy Tan.

Amy's mother is talking in that line... I think a fuller quote is more illustrative: "...inside you must always be Chinese. You must be proud you are different. Your only shame is to have shame."

What her mother is saying is that being different is not something to be ashamed of. There should be nothing embarassing about just being Chinese or honoring her ancestral culture. Rather, the fact that she is ashamed of her family and their customs says something about Amy... something not complimentary at all. No matter how much she pretends to be an American, Amy IS Chinese and there's nothing she can do about it. To her mother, it is the pretense that her heritage is wrong and irrelevant that is the real crime.

So another way of saying the same thing might be, 'there is nothing wrong with being different, but it is a bad thing to be ashamed of who you are'. Hope that helps!