What could it possibly mean?

It's either because she has no doubt the baby is his, or she knows damn well the baby is not his, i would say the latter. If beyond reasonable doubt she thought the baby was his she would not hesitate in having a test. does he not see the baby at all so he can have a test done. And then if the baby was not his he would not have any responsibility to the child. Then the mother could go after the baby's real father (or does she not know who the baby's father is ) i would contact a solicitor to legally make her have the test.