You may insist otherwise, but the speaker is certain that Katherine belongs to them. They believe their connection is undeniable, fueled by intense emotions that they can't ignore, whether they label it as passion or obsession. This insistence underscores a deep, consuming desire that defines their relationship.
The speaker emphasizes that their feelings are overwhelming and persistent, making it impossible for them to let Katherine go. They view their bond as something inevitable and powerful, highlighting a sense of possession and an unwavering commitment to hold onto her regardless of any objections.