Breakdown
X-23 was an assassin, designed to be the ultimate weapon. And she came to this mansion (a place where kids her age and older seemed so...normal and happy; she'd felt quite a few twinges of jealousy watching them) seeking revenge on the man who made that happen.
But when Wolverine told her that he was probably the closest thing she had to family, X-23 momentarily forgot her objective as tears, for the second time in less than an hour, spilled down her face.
It wasn't true; it couldn't be true, no matter how much she wished it. She was trained from birth as a weapon, a monster. Monsters weren't supposed to have something as human as emotions, and monsters certainly didn't have families.
X-23, continuing to cry, barely registered, not only what Wolverine was saying, but also the hand that he'd placed on her back.