Yeah you’re definitely closer to what I’m trying to say.

Basically, the argument is that (as RL stated earlier) Rey is of “purer intent” than Kylo - she’s fighting for the light and him the dark. He had a chance to take the mantle of ‘hero Skywalker’ but chose the dark path. The saber represents and recalls the weapon of the savior of the galaxy, in the PT it belongs to the “one who will bring balance,” and in the OT it belongs to the “last hope.” In the ST, the saber is metaphorical of the new mission to reignite the spark of hope and take up the fight (this is pretty explicit in TLJ, less so TFA because of rewrites). Kylo wants the saber because of his birthright, but what it represents doesn’t belong to him, it belongs to Rey. So when the lightsaber goes into Rey’s hand and not Kylo’s, in my mind the literal question of “how did it get there?” -whether the answer is that Rey is stronger in the force, Kylo was caught off guard, or the force is exerting its will - doesn’t matter. What matters is the figurative meaning of the scene - Rey has finally taken up the saber and the mantle it represents which she initially rejected, and which at this point she is more deserving of than Kylo due to who she is, and not who her parents are.