There could be a few reasons.
1. What you owe is probably self-employment taxes not income tax. So if you have self employment income of $20,000 and you are married filing jointly, you have SE taxes of $3,060, but you would not have any tax liability for ordinary income taxes because your taxable income after your standard deduction would be $0.
2. If your tax on line 16 of your 1040 is $0, then you would not be eligible for the child tax credit as that is a non-refundable credit which means it will reduce your taxes to $0 but not below.
If you are not eligible for the Child Tax Credit, it is possible to get the Additional Child Tax Credit which is limited to 15% of your earned income over $2,500. So if your earned income is $12,500, the credit would be limited to $1,500.
Basically, Your credit is likely limited due to your income, but since self-employment taxes are calculated separately, you will still have to pay them.
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