Okay, so I've seen a bunch of these 'rejected mate' stories, and the drive is usually a messy cocktail of things. It's rarely one clean motive. In a lot of them, the initial push is pure, stubborn pride—he can't accept that she said no, that she walked away from what he sees as a destined bond. It feels like a personal insult to his status, his wolf, everything. But then, if the writing's any good, that pride gets eroded fast by genuine remorse. He starts seeing her strength, how she's surviving without him, and that obsessive chase morphs from 'I claim you' to 'I don't deserve you, but I need to fix what I broke.' The fear of her moving on with someone else is a massive, often unspoken, fuel. It's less about love at first and more about a desperate need to correct a cosmic mistake he feels responsible for.
Sometimes the magic of the bond itself is a physical compulsion, an ache that won't quit, which adds a layer of biological urgency to the whole psychological drama. He's not just heartbroken; he's literally unwell without her, which makes the chase frantic and borderline irrational. The best versions show him realizing he has to become someone worthy of her, not just force the bond to snap back into place.