Which reinforces the point that he is a stranger/enemy she barely knows. What she does know is that he has tried to open a gate to hell, and that he has tried to kill his own brother.

In regards to not caring about his lineage, that seems contradictory to her position as a demon hunter that has declared that she still wants to eliminate all demons. Dante is a lone exception to this rule, and his show of compassion would not carry over to Vergil.