If you want to buy insurance from them, yes. There is no right to buy insurance from any given company, and no obligation on the part of any company to sell insurance (either generally--they are voluntarily in the business, after all, and not required by law to be insurers or provide insurance--or to you specifically). If you don't like what this insurer asks for or requires, you can refuse to do business with them and try to see if you can find an insurer who does not require the SSN.