SSN is not for identification
Social Security Cards remain property of the federal government. You, if you were issued one, are the custodian of government property. You have a duty to responsibly use what they entrusted to you. It was issued for government purposes. Not for other uses. The original cards stated, in bold capitalized red letters, “NOT FOR IDENTIFICATION“.
I would tell anyone asking for a number:
SSNs are not for identification. A SSN is a government number created for government use. You are not the government. You are asking for protected personal identifiable information as defined in Title 2, U.S. Code of Federal Regulations, Section 200.1.
The Social Security Administration brochure 05-10002 Your Social Security Card and Number, tells people to ask what law requires them to give a number.