Say mom has traits A-B,C-D, and E-F. Dad has traits U-V,W-X, and Y-Z. Child is B-U,D-W,and E-Z. Paternity is likely.
Child is B-L, D-M, and E-O? Paternity impossible. You know the traits that show up in the child came from neither the father or the mother (L, M and N). It is harder (but not at all impossible) to do it from just the father and the child. But it takes more work because you don't know if something the child has that the father doesn't didn't just come from the mother. But if after checking a few loci where the child has two traits, neither of which is present in the father........well you begin to establish that he is not the actual father.
Thanks for the explanation!
My thinking is that tests like this are rarely done to determine who Mom is. After all, Mom has the baby in her arms.
But then, I am totally willing to defer to the voice of knowledge, since I have zip to offer on this subject. :)
My head hurts!