If I can't claim someone as a dependent why must I give there SSI number?

The Internal Revenue Code of the Untied States requires that to claim someone as a dependent you must enter their Social Security number or the ITIN that was issued by the IRS.

If you cannot claim someone as a dependent then do not enter them on your tax return.

What are you trying to do?   If you are not filing with a spouse -- whose SSN you must enter-- or claiming a dependent, then who are you entering on your tax return?  Why?    Whose SSN are you concerned about and why would they even be on your return?    Unless you mean you are trying to enter the childcare credit.  Then you have to enter the SSN or Tax ID of the childcare provider.