It's codified in the TSA travel document SOP that the only acceptable forms of state issued ID, are those issued by the DMV or equivalent state office for the sole purpose of identification, and not for evidence of any other status. Your SDA permit is expressly issued for the purpose of identifying your status as someone who's authorized to carry concealed, therefore it's not on the approved list. It may be used in conjunction with other forms of ID to verify identity in the event your primary ID is lost or stolen, but it isn't supposed to be accepted as a primary ID for identification purposes during travel.
Before you go complaining that this is a stupid rule, please remember that the correct avenue for expressing said complaint is your elected representative!
Before you go complaining that this is a stupid rule, please remember that the correct avenue for expressing said complaint is your elected representative!