If TurboTax (TT) is allowing you to claim him as a dependent (under the Qualifying Relative rules; he is too old for the qualifying child rules) but is not giving you the tuition credit, the most likely explanation is that your income is too high (> $90K, $180K married filing jointly) to qualify for the credit.
If that is the case, it may be better for him to claim the tuition credit on his return. You will lose the $500 Dependent Credit, but the tuition credit may be worth as much as $1000 to him depending on his student status, tuition paid and whether the American Opportunity Credit (AOC) has already been claimed four times in the past (by either him or his parents). He must be a half time or more, undergraduate degree candidate. The AOC is usually worth as much as $2500, but is only 40% refundable ($1000 max).
The less generous Lifetime Learning Credit (LLC) is worth up $2000. It has the same income limit as the AOC, but there is no limit on amount of times it can be claimed, but it is not refundable (it can only reduce an actual tax liability; unlikely if he qualifies as your dependent).
