Q. Do I not qualify for it or am I missing to answer something in TT?
A. Based on your description, you do qualify (your earned income is more that half your support). You've answered something wrong in the interview.
When TurboTax sees that you are a FT student, under 24, it will add the earned income support question to the interview. The earned income support question is part of the personal info interview, not the education interview.
Go thru the personal info section again and be sure you answered that question correctly (or you answered the preceding questions correctly to generate that question).
That said, it's not that clear that that you do provide more than half your own support.
The support value of the home, provided by the parent, is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants.
The IRS has a worksheet that can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf
