Imma share the theory I've been developing about this very point. How does Rey beat Kylo at getting the saber out of the snow?
MAJOR FUCKING SPOILERS AHEAD ... SO BE WARNED!!!! I'm not spoiler tagging a massive block of text.
Theory 1 - The saber wants to go to Rey. It might have actually resisted Kylo. I know that sounds ridiculous, but this is part of the theory. The saber called out to Rey and she had flashback images when she touched it. I think it's going to be revealed in future movies that Vader's mask called out to Kylo. That's why he still has it and that's why he talks to it when he's feeling particularly emo. Both items (saber and mask) were Anakins. They represent his light and dark sides. I think they're going to introduce the idea that objects (relics) can retain some elements of the force from their owner. These items have a limited ability to communicate with people.
Theory 2 - Rey was the better padawan. I posit that Rey and Kylo/Ben were students of Luke. Rey was better than Kylo. She could beat him at most training exercises including saber fights, force pulling, etc. Kylo wanted to be the best and he got frustrated because Rey became Luke's favourite student. Kylo became emo kid and tore the shit out of the jedi temple. Part of this theory is that Luke manages to save Rey and escape with her. Luke force blocks her memories (TFA has introduced how much the force can be used to fuck with people's minds) and leaves her on Jakku. He instructs some people to look after her and tells Han to stay close by. That's how Han shows up so quickly after she takes the Falcon. Han knew damned well where his precious ship was!!! All of this also explains how she becomes so powerful so quickly ... and before people say "but she had memories of being a little kid" I'd suggest that the memory is fake. Planted by Luke.
For me, theory 1 and 2 aren't independent. They work together, because of one simple fact: I think Rey is Rey Solo, not Rey Skywalker. It's too obvious for Rey to be Luke's kid. They force wiped her memories to protect her from Snoke and Kylo. Leia and Han were in on it. Rey has to be related to Anakin, which is why the saber called out to her. It's why Leia hugs her after Han's death.
Anyway, that's the theory. Probably half wrong but I like it.
ALSO SPOILERS, bonus thought ... I think everyone will like this:
There's no precedent for force users connecting minds with non-force users. So when Leia feels Han's death, she's not got that sense from Han. She got it from Kylo (her son) or Rey (who was watching). That connection could reveal Rey as her daughter and could be the 2nd reason for the hug after Han's death.
Ok, I'm done ... feel free to shoot me down! :)