I understand you perfectly - I'm watching it for the 3rd time in 2 weeks! ? I recommend you read the story https://my.w.tt/ybKYKkDjt5. It's equally entertaining!
To answer your question, the reason why he bled the moment she broke the frost petal is because he loves her and that petal was a part of her real self, offered to him as a token of her love. He used to keep it safe within one of his souls, so when she hurt herself, she hurt him too, signifying that they are one. At least, that's how I interpret the scene.