It would be nice if you gave a few more details to help with your case:
We can only work with what you have given us; assume the rest:
You are angry and frustrated because the Appraisal came in lower than the Offered price; which means that both you and the Buyer are valuing the house at higher than Market.
Unfortunate for you; most Appraisals are really close to Market; the Bank really wants the deal to go through; they really do.
So, if you won't lower your asking price, you are telling the Buyer that you are standing firm, and won't sell. The Buyer probably has no choice; they will go away.
So, the Buyer is out some money and you have to start over again.
Oh, and there is no such thing as "Seller's Rights".