Should I receive a 1099 for tuition paid to me by an individual who attended a class that I taught?

An individual who attended a class that I taught and paid me tuition for the class wants to deduct the tuition they paid me as a business expense on their business return. They want to issue me a 1099 for the tuition they paid. I believe I should be giving them an itemized receipt And they can use it as a business expense anyway they wish to, but that they should not be issuing me a 1099 nor should they have my Social Security number. I am an independent contractor and file a schedule C.