There is no such rule. You must be misunderstanding something.

The child tax credit  (CTC) is  limited to your tax liability. The CTC is a non-refundable credit and can only reduce your income tax to 0, It can not help you beyond eliminating your tax liability. But, if you have more than $2500 of earned income, some or all of it is usually given back to you thru the "Additional Child tax credit". That is, part of the CTC may be on line 18b of form 1040 (2019 version) instead of line 13a (lines 17 and 12 in 2018).   The  ACTC is calculated on form 8812 and  is basically 15% of your earned income over $2500. The ACTC is a maximum of $1400 per child (not $2000).

The child tax credit is on different lines, on the 2019 form 1040, than it was on the 2018 form.  See item #4 below.

 There are 6 possible reasons; you aren’t getting the Child Tax credit (CTC). It’s usually #4:

1. You’ve entered something wrong. In the personal Info section, for the dependent, you must select answers that indicate that he/she is your dependent child. If the child was born during the year, say he/she lived with you all year (note: TurboTax changed how this section is done two years ago, you may need to go thru the interview again or even delete your dependent and start over). If the child was born in 2018, you have to answer that he lived with you all year. The CTC is not an automatic $2000, per child. It is income dependent. If you haven't entered your income yet, the CTC will not show.
2. Your child may be too old (over 16). You can still claim your child. What you can't claim is the Child tax credit. This comes as a big surprise to many parents the year their child turns 17. A child over age 16 no longer qualifies for the Child Tax credit (CTC). Although a child can still be a student dependent through age 23, and a qualifying child for EIC, the Child Tax Credit expires the year they turn 17 and you no longer get the $2000 CTC.
3. Your income is too high. The Child Tax Credit (CTC) is phased out at higher incomes starting at $400,000 for joint filers ($200K single). You lose $50 for each $1000 (rounding up) your income is over that threshold.
4. Your income is too low. The child tax credit (CTC) is also limited to your tax liability. The CTC is a non-refundable credit and can only reduce your income tax to 0, It can not help you beyond eliminating your tax liability. But, if you have more than $2500 of earned income, some or all of it is usually given back to you thru the "Additional Child tax credit". That is, part of the CTC may be on line 18b of form 1040 (2019 version) instead of line 13a (lines 17 and 12 in 2018).   The  ACTC is calculated on form 8812 and  is basically 15% of your earned income over $2500. The ACTC is a maximum of $1400 per child (not $2000).
5. You are the custodial parent and the non-custodial parent is claiming the dependent this year. The CTC goes with the dependency, even though the custodial parent still gets the Earned Income Credit, Dependent care credit and Head of Household.
   6. Another possibility is that part of your tax due is not regular income tax, but is self-employment, early distribution penalty or another type of additional tax, for which the CTC cannot be used.

There has been lots of hype in the news about the new $2000 Child Tax Credit.  Unfortunately, some people do not yet understand that it does not mean they will automatically receive $2000 per child just for filing a tax return.

Do not assume your refund will include $2000 per child for child tax credits.  It does not work that way.  The CTC is used first to reduce your tax liability to zero. After that, there is a refundable portion —up to $1400 — called the Additional Child Tax Credit that is calculated based on the amount of income you earned.  You do not necessarily get the maximum amount.  You get 15% of the amount of income earned above $2500--UP to the maximum amount possible.

Thank you for the response. The key issue appears to be my source of income: I am self-employed. Would you (or others) know what the controlling Treasury Regulation is?

No matter what your income is the credit has limitations ... look at the CTC form and the program worksheets to see how the rules affect your credit.  And go back and review that screen you saw... maybe it will make more sense after looking at the return itself. 

You can peek at only  the Federal form 1040 and the summary of the state info by going here:

1) lower- Left side of the screen...click to the left side of the "Tax Tools" text selection.
2)  then select "Tools"
3) then select "View Tax Summary" from the pop-up
4) then back to the left-side and "Preview 1040"

Then hit the "Back" on the left side to get back to your tax entries.

To view your entire return using the online editions (including the state) before you file, you will need to pay for your online account.

To pay the TurboTax online account fees by credit card, without completing the 2018 return at this time, click on Tax Tools >>> Tools  and then Print Center.  Then click on Print, save or preview this year's return.  On the next page, to pay by credit card, click Continue.  On the next screen it will ask if you want Audit Defense, if you do not want this option just click on the Continue button.  The next screen will ask for all your credit card information so you can pay for the account.

There was lots of hype in the news about the new $2000 Child Tax Credit when the tax law changed for 2018 and beyond.    Unfortunately, some people do not yet understand that it does not mean they will automatically receive $2000 per child just for filing a tax return.

Do not assume your refund will include $2000 per child for child tax credits.  It does not work that way.  The CTC is used first to reduce your tax liability to zero. After that, there is a refundable portion —up to $1400 — called the Additional Child Tax Credit that is calculated based on the amount of income you earned.  You do not necessarily get the maximum amount.  You get 15% of the amount of income earned above $2500--UP to the maximum amount possible.

If your child turned 17 in 2019, even on the last day of 2019, you do not get the child tax credit.  There are no exceptions to the rule.  You can still claim your child as a dependent.

Your child must have a Social Security number to get the CTC. 

If your child was born in 2019 you need to say the child lived with you for the WHOLE year.

If your child lived with you for less than half the year you cannot get CTC.

If you did not earn at least $2500 you cannot receive the child tax credit.  Beyond that amount the CTC you receive is affected by your tax liability and the amount you earned.  You might not get the full $2000 of CTC.

Look at your 2019 Form 1040 to see the child--related credits you received

Child Tax Credit line 13a

Credit for Other Dependents line 13a

Earned Income Credit line 18a

Additional Child Tax Credit line 18b

Child and Dependent Care Credit line 18d

Even though it can reduce your regular income tax to zero, you will still owe any self employment tax on your Schedule C Net Profit.

"Self Employment tax" (SET) is how the self employed pay social security and medicare (FICA) tax.  No credits can be used to reduce your FICA.  Credits can only be used against income tax. The fact that the self employed pay their FICA  (as SET) at tax filing time, instead of having it taken out of their pay check,  does not entitle you to apply unused tax credits, to reduce it.

Some say FICA is not really a tax, it's a contribution toward your retirement. So no credits can be used. FICA = Federal Insurance CONTRIBUTIONS Act

I don't think anybody here is going to have a ready reference to a section of the tax code.  But, just note the flow on form 1040. The non refundable credits are applied after income tax is calculated, but before SET is added.