It's sounds like your tax liability (line 11b of form 1040) is low enough that it is only taking one tax credit to get your tax to zero.
That said, it's usually the education (tuition) credit that goes away, not the credit for other dependents. You have to look at the form 1040, to see what's going on. Look at lines 11b, 13a & 13b of form 1040 and lines 3 and 7 of Schedule 3.
