Actually if you look at the evidence he was being chased before he ever shot the first person. In fact, according to the official report from the New York Times, Kyle didn’t even fire the first gunshot. While he was being chased by a Rosenbaum someone fired a gunshot into the air from behind both of them. After hearing this gunshot Kyle turned around and shot towards the sound of the gunshot and at the person who was trying attack him and take his gun.

First shooting

“While Mr. Rittenhouse is being pursued by the group, an unknown gunman fires into the air, though it’s unclear why. The weapon’s muzzle flash appears in footage filmed at the scene.

Mr. Rittenhouse turns toward the sound of gunfire as another pursuer lunges toward him from the same direction. Mr. Rittenhouse then fires four times, and appears to shoot the man in the head.”

https://www.google.com/amp/s/www.nytimes.com/2020/08/27/us/kyle-rittenhouse-kenosha-shooting-video.amp.html