From what you wrote it's not clear whether your customer operates a business. If the work you did was strictly for their home, not for their business, they are not supposed to issue a 1099-NEC for personal expenses. They may be trying to claim the work on their home as a business expense. That, of course, is not legitimate if the part of the home where you installed the flooring is not used for their business. Or they might just be confused, as xmasbaby0 said. But if they do have a business and the part of the home where you installed the flooring is used for their business, it is a legitimate business expense and they do have to issue a 1099-NEC to you.
In any case, the path of least resistance for you is to just give them your EIN and let them issue the 1099-NEC. I don't see any harm to you in doing that. You have to report the income whether or not you get a 1099-NEC. You do not have to be concerned about what they do on their tax return. And if it is a legitimate business expense for them and you do not give them your EIN it will cause problems for you.
