Why don't I get a dependent claim of my son for 2015 just because he 18 in 2016?

You claim him as a dependent until he is age 19 on federal tax returns. Maybe you are thinking of the Child Tax Credit? That's a different item where he would have to be under 17 at the end of 2015.

What do you mean by "dependent claim"? Are you referring to claiming him as a dependent on your taxes? The child tax credit? A dependent on your health insurance?