Well, the young Dr was absolutely potty & believed that she was his long lost sister because she'd said that her parents were killed in a car crash. She wasn't his sister, his actual sister was in a psychiatric hospital & had been from the age of 5 when their parents died. Kate's parents were shot by someone who broke into their house & she'd got away by running & hiding.
The young Dr intended to kill her & then himself...so that, in his mind, he could protect & not be parted from her as they had when they were kids.
He didn't get to kill her in the end & got shot by the cops (cos as in every show like this, the detective realised he was the murderer at the last minute!!)
That was it really, I was a bit weird & I didn't really get the point.