It would seem best if neither I nor my son claimed him.
There are limited circumstances when you would want to not claim him (but, yes you are allowed to not claim him). Letting him claim the education credit would be one (see below). There is no more personal exemption. "Not claiming himself" is just a matter of checking a box on form 1040 saying that somebody else CAN claim him. He does not indicate anywhere on the IRS forms whether somebody will actually claim him (but he does indicate that in TurboTax).
While technically there is a provision that allows your student-dependent to claim a federal tuition credit, from a practical matter it seldom works out. A full time student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit (AOTC) if he supports himself by working. He cannot be supporting himself on student loans & grants and 529 plans and parental support. It is usually best if the parent claims that credit.
If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit. The student must still indicate that he can be claimed as a dependent, on his return. This is worth up to $2500 (AOTC shifts to all non refundable)
