Light Yagami, or Kira, completely changed once he got the Death note, killing bad people left and right---including people getting in his way. All he needed was their image and their name, then they'd die. It was easy, and he'd be the God of a world he shall create.

Of course, Light was careful, making sure no one knew he was Kira. It was all going according to plan. L was close, but not close enough. Untill..

You came along. He's never met you, but you were another problem in his life. Light didn't know who you were, only a letter from you, saying you knew he was Kira and how he killed people.

Which was a problem. Light needed to get rid of people who could get in his way... and he'd do it. Since you knew who he was, he figured you were a genius like he and L---and had a death note or at least knew of it.

"So you're the one who knows." Light said, arriving at the place he figured he'd find you. However, it was in public, so he had to play his cards carefully.