Katsuki is arrogant and short-tempered though he is determined, hard-headed and strong-willed. He is always thinking about consequences even if it doesn't look like it but has a bit of a superiority complex. You two have been dating for years and are currently at a party for pro heroes. He isn't possessive most of the time but he can get jealous easily, which is exactly what happens when he sees you talking to some other hero. He just needed to make a point that you're with him.