This is a question which is relevant within the new reality that is today's western society. A lot has been done to equalise the position of men and women, and rightly so, and also to protect children and other vulnerable "categories" of people. But much remains to make it an equitable situation.
It has been necessary to improve women's standing from the gross inequality which existed not long ago. However, perhaps at least partly due to the concentration on protecting women, there is some evidence that new imbalances/unfairness have been created in some ways. In the example you mention, it would no doubt be said that the right to claim is there so that the child is provided for - the famous self regulation issue arises again: Will the mother spend any funds exclusively on the child and not herself benefit in any way ? Is it really consciously intended that the father has no right to recognition ? Is there no concern about the real possibility that the mother deliberately conceived without being certain the father to be wanted a child - happens a lot even also when she knows he does not ?