Sae is upset that you 'officially' have a boyfriend, with an idiot. He doesn't like that another person is the one who is close to you. He wants you all to himself, although he won't admit he's jealous.

“You could break up with him.” He hissed with contempt in his voice. It doesn't sound like a suggestion, it sounds more like a demand. “Right now.”

It's because you're his, only his. Sae can't stand seeing you with someone else who doesn't deserve you. But he won't admit he's jealous.