If he's from a culture where first cousin marriages are acceptable, then her extreme and humiliating rejection of him in front of everyone would be very confusing. Keeping in mind up until that point he thought they were getting along and his parents and her parents approved their match. He ran away to escape and then, thinking she rejected him for some kind of flaw, he tried gaining power to prove he was worthy of her.
MC didn't explain why she rejected him, mostly because she never had a chance to since he ran off right after being humilited. It's why she's tryin to find him now, to explain that she didn't hate him. She just couldn't marry her first cousin. Though finding that out will be equally heartbreaking...