Why do you think you do not qualify for the AOTC? Being under 24 does not automatically disqualify you. What disqualifies you is being full time, unmarried student, under age 24, who did not provide more than half his/her own support with earned income.
Here's more bad news: this is, most likely, NOT TurboTax's mistake. After it detects your age and FT student status, it asks you the support question. You, most likely, answered that wrong. The most common mistake is you read it as "did you provide more than half your own support" rather than "did you provide more than half your own support with earned income".
That brings up another issue: If you did not meet the support test, why are you not your parent's dependent? It is usually best if the parent claims that credit.
