Why I cant I claim the american opportunity credit? I claimed it my first 3 years of school, but this year Turbo Tax is making use the tuition deduction which I get less

If you are eligible, you have answered  something wrong, in the interview. But, a lot of people are just not eligible. See https://www.irs.gov/Individuals/AOTC

It may be that you did it wrong the last three years.  

 A full time unmarried student, under age 24, even if you don't qualify as a dependent, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself with earned income  (by working) .  You cannot be supporting yourself on parental support, 529 plans or student loans & grants. You usually must have actually paid tuition, not had it paid by scholarships & grants.  Your $5700 of earned income is obviously less than half your support.  It is usually best if the parent claims that credit. 

You cannot claim a credit if you are, or can be, claimed as a dependent by someone else.