Why does my child have to pay tax on 529 distribution

You've entered something wrong*.  Since you know it's fully covered by expenses, just don't enter the 1099-Q (or delete it if you've already entered it).

You can just not report the 1099-Q, at all, if your student-beneficiary has sufficient educational expenses, including room & board (even if he lives at home) to cover the distribution. When the box 1 amount on form 1099-Q is fully covered by expenses, TurboTax will enter nothing about the 1099-Q on the actual tax forms. But, it will prepare a 1099-Q worksheet for your records. You would still have to do the math to see if there were enough expenses left over for you to claim the tuition credit. You also cannot count expenses that were paid by tax free scholarships. You cannot double dip! 

On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution." 

You can claim the tuition credit, even though expenses were paid by a 529 plan.  Use $4000 of  the tuition paid for the credit and use books, computers and room and board   for the 529.

*One possibility is that TurboTax allocated part of your dependent's college expenses to claim the Tuition credit, even if you are not eligible or otherwise did not claim it. That reduces the amount that can be used to claim the  529 earnings, shown on the 1099-Q, as being totally tax free. Go through the entire education interview until you reach a screen titled "Your Education Expenses Summary".  Click edit next to the student's name. That should take you to a screen “Here’s your Education Summary”. Click edit next to “Education Information”. When you get to the screen titled “Amount Used to Calculate Education Deduction or Credit”, verify the amount you want to use or change it.  You may reach that screen sooner.

Another possibility is that you had scholarships that TurboTax allocated some of the expenses to.   To make some of the scholarship taxable (re-allocate some of the expenses), you must tell TT how much you want taxable by saying it was used for room &board. Note the wording at that screen “or other expenses”. You didn’t have to literally use the scholarship for R&B.