It sounds like neither you or your son have been required to file a state or Federal tax return for 2018 or 2019.  In the eyes of the IRS your son is not a dependent if he is not claimed as a dependent on a Federal tax return.

You will receive a stimulus check if you:

• Have a Social Security number.
• Have filed taxes in 2018 or 2019, or don't earn enough to file but receive Social Security payments.
• Earned less than $99,000 for single filers, $136,500 for heads of household, or $198,000 for married filers according to the most recent tax return filed.
• Are not claimed by someone else as a dependent.

he doesn't provide half of his own support because Social security doesn't count.

As long as he is under 24 and a student at the end of the tax year, he is your qualifying child.