...Carver is Rebecca's child's father. I knew it!
I called it! That was the reason he is after the group. That's why he doesn't just shoot up the place instead of knocking on the door. He doesn't want Rebecca to die with his baby. I'll also call that she didn't conceive it willingly. Since she was the only grown woman in the group, he probably felt he had to carry his legacy on somehow and raped her. Everyone was disgusted by what he did, and left him.
That's why Rebecca is so bitter! I'm glad I wasn't mean to her about her baby now.
And judging by ep3 slider where they're in a prison, Rebecca and Clem are going to be captured in the future and probably kept around until she goes into labor.