Young Ben Solo grows up hearing about Darth Vader, how he was once a good Jedi who became an evil Sith, how his parents fought against him. Despite his final acts, even Uncle Luke has to admit that he has caused much suffering in the world, that will never bee erased.
So when young Ben Solo starts showing signs of being Force sensitive, he is terrified of turning to the Dark Side. So much so that he just can't deal with it, and any dark thought/temptation he pushes to the side. Until he cracks, and an alter is created to shoulder all that weight: Kylo Ren.
The more Ben refuses to deal with the Dark Side, the stronger Kylo gets. All the way until the point where Snoke finds him, and that's the last time Ben is in full control of his body.
So when Kylo tells Han he isn't anything to him, he isn't lying. He is not Ben Solo.
Kylo Ren is Ben Solo's alernate personnality
So when young Ben Solo starts showing signs of being Force sensitive, he is terrified of turning to the Dark Side. So much so that he just can't deal with it, and any dark thought/temptation he pushes to the side. Until he cracks, and an alter is created to shoulder all that weight: Kylo Ren.
The more Ben refuses to deal with the Dark Side, the stronger Kylo gets. All the way until the point where Snoke finds him, and that's the last time Ben is in full control of his body.
So when Kylo tells Han he isn't anything to him, he isn't lying. He is not Ben Solo.