Can I really not claim my 21 yo college student if he made $6000 in his summer job 2016?

If your child was a full time student his income amount does not matter.

You can claim him as a dependent as long as you can answer YES to these questions.

• Do they meet the age requirement? Your child must be under age 19 or, if a full-time student, under age 24. There is no age limit if your child is permanently and totally disabled.
• Do they live with you? Your child must live with you for more than half the year, but several exceptions apply. Being away for school does not change the child's permanent home address and they still qualify as being in the home.
• Do you financially support them? Your child may have a job, but that job cannot provide more than half of her support.
• Are you the only person claiming them? This requirement commonly applies to children of divorced parents. Here you must use the “tie breaker rules,” which are found in IRS Publication 501. These rules establish income, parentage and residency requirements for claiming a child.

https://ttlc.intuit.com/replies/3302077

If he made more than $6,300 W-2 income or $400 self employment then he must file a return. Anything less he is not required but it is a good idea to file a return to get back withholding. Be sure he selects someone else can claim him as a dependent on his return if he files.