Deductions & credits

Unless your income level is too high you would get $500 in credit for other dependents.  If he is eligible for education credit that may explain why he does better if you don’t claim him but unless your income is too high you would be better off claiming that credit. In either case you will run into the Kiddie Tax. 

https://ttlc.intuit.com/community/income/help/what-is-the-kiddie-tax/00/25913/amp