Makes sense to me. According to the law, minors (under 18) cannot be held legally responsible for their actions, behavior, or well-being. In a lounge setting where customers are expecting a place of rest, relaxation, or productivity, minors should not be present without a supervising adult.

Furthermore, if a person under 18 were to become injured or ill while in a club, the airline could be sued if there were nobody supervising or attending to the needs of the minor. It's not the same as having status or flying premium cabins, which minors can do on their own (including the OP). Here's why. While travelers of all ages are proceeding through the airport terminal, there are employees specifically looking out for them (agents, security, police, TSA, etc) as well as on board (crew members). However, the same does not apply in the secluded conditions of a lounge. If you were having a medical problem, you could find a quiet corner of a lounge and it's possible nobody would notice for hours. If the person were an unaccompanied minor, it could be the airline's liability.

IMHO, for good reason, AA does not sell Admirals Clubs memberships to persons under 18, nor allow anyone under 18 into the clubs unless accompanied by a supervising adult. (I remember purchasing my first year of AC membership just a few days after I turned 18 and became eligible!)

The Flagship Lounge rule prohibiting access to unaccompanied persons under 21 is probably because of the self-service alcohol. The 50 states of the USA have enacted state laws that prohibit alcohol purchase/possession by persons under 21, with very few exceptions.