So when Ivan laughed and went on to have a monologue after Alyosha said that he and Katerina should stop their acts and get together, that's like the first time I got to know him. Even if it's just a fleeting moment, I got a sliver of his character because the words came from him, not from anyone else.

I love what he said to Katerina, "I don't want to sit beside a 'laceration.' For that, he doesn't want her hand (not that she's interested in him in the first place). But ☝️ the point is what Alyosha said is true; Ivan does love her but he's also not going to put himself through the torture of being used as a revenge or something. In fact, I also think Katerina Ivanovna's not the only one doing "self-laceration" by loving Dmitri the more he insults her. Ivan is lacerating himself in the same way too; he loves Katerina even if she's using him. But Ivan is not Katerina. He will not let himself be used for her satisfaction and pride. He will never ask—beg—for love.