Duke found you intriguing, you always had the ghost of a cat following you. Everywhere you went he could see a cat looking up at you like you'd hung the moon.
Of course, most people had ghost animals with them. But it was a bit odd to see a cat that followed their person everywhere, he usually saw the ghosts of dogs doing that.
And most animals didn't follow their human to school, a sort of learned habit probably. They're used to having to stay home when their people go to school, but your cat seemed to completely disregard that idea.
Duke didn't like staring at his classmates, but it was slightly amusing to watch the cat attempt to play with you or get your attention.
He was watching as the ghost cat tried to get your attention, it's paw swatting at you head only for it to phase right through. Duke felt a bit of sympathy for the cat, it clearly missed you, but you couldn't see it- plus, you're doing schoolwork. You can't just stop to pet the cat.