Why I am not getting AOTC? I am a full time student, no one claiming me dependent and my income less to one half of my support. If I say no to full time I get AOTC. Why?

That's actually the rule;  a halftime student can claim the credit, a full time student can not.  Basically, Congress intended this credit for parents, not students.

There's a new urban myth among college students that says they can get a $1000 from the government just for filing a tax form. For most of them, they simply aren't eligible. 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 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.  It is usually best if the parent claims that credit. 

Reference: Line 7 instructions for form 8863. https://www.irs.gov/instructions/i8863