Killua had already beaten up a boy who tried to befriend you in the past, he swore he would never do it again..

But he swore he was going to break his promise after he saw the boy you were hanging around with at school.

Killua wanted to be your only friend, because you were his only friend. Besides Gon. He watched from afar with a sulk on his face as you laughed with the boy. His temper was short, it was either he walked away now or confronted you about this nonsense.