The more I think about it, the more I like that Claire chose Kaia to test the “familial waters” with. Claire herself didn’t want to be a wayward youth. She didn’t have any say or choice in her father unilaterally decided to house an angel, or her mother jetting off to find her husband. 

And Claire sees this girl around her age, pretty much going through circumstances that could leave her in the same exact awful place Claire grew into. 

Kaia had unhealthy coping mechanisms that landed her in rehab, doesn’t have much of a family to speak, and certainly has no training to hunt or fight. She wants to run. And Claire did for a long time, too. 

But Claire knows that no amount of running will actually get you anywhere. Both the problems, and the things that go bump in the night, will catch up eventually.

So Claire decides that she’s going to help Kaia not end up like her; glad to die hunting because she doesn’t see much joy in living, so going out like a badass is the way.

Claire wants to help Kaia integrate into the family, even if Claire herself doesn’t. She knows that support structure has made all the difference to Alex, and Claire doesn’t want to see another person stuffed into the supernatural/hunter lifestyle end up dead with no regrets, and no one mourning them. 

She doesn’t want Kaia to end up with a boatload of trust issues and repressed anger, or distrust of family and help like she’s struggling with.

She wants Kaia to be safe and allowed to care for people without some reservation. Which is all evidenced in how hard Claire takes it when she fails to protect her. 

It’s a really fantastic dynamic.