alanabit has just written pretty well what I would have.

I think that mechanically transposing rights and obligations between fathers and mothers in this kind of situation is wrong. As alanabit pointed out, men don't get pregnant, carry babies within them, and give birth. That's a significant difference.

I note this time jeffp mentioned the right of a child to know her or his father, and that's a real right, I accept; but I think it's not a right which necessarily overrules everything at all stages of life. If a mother in this situation were to decide that one man would make a terrible father and another would be far better, I wouldn't be inclined to blame her for picking the more suitable one, and dispensing with the tests that would prove things one way or another.