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I haven't read the whole article, but the paragraph on the sequence of the shooting doesn't seem to be an objective account or entirely consistent with the video.
Given the reputation for editorial thoroughness at the New York, the mixed-use of protester, demonstrator, and rioter doesn't seem to have been particularly thought through.
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While the video failed to mention comments on his apparent lack of knowledge on the photo of him with proud boys or making the OK sign. So maybe neither is complete. But the video seems more willing to avoid evidence that he was and isn't a white supremecist or in alignment with groups.
Thought looking again I think it says what the video shows?
During the chaos, Rittenhouse moved down the street toward Car Source’s second mechanic shop, where rioters had been smashing car windows. He crossed paths with the angry bald man, who chased him into the shop’s parking area. The man now wore his T-shirt as a head wrap and face mask, leaving his torso bare. Screaming “Fuck you!,” he threw his plastic bag at Rittenhouse’s back. Rittenhouse, holding his rifle, reached some parked cars just as a protester fired a warning shot into the sky. Rittenhouse whirled; the bald man lunged; Rittenhouse fired, four times. The man fell in front of a Buick, wounded in the groin, back, thigh, hand, and head.
In the video it doesn't seem like Huber hits him with a skateboard at all, more stumbles over onto him with it.
That said, the shooting of Rosenbaum is more understandable if repugnant. Someone is chasing you, you hear a shot from behind you, you are jumped on and so you shoot in - self-defense. From there it all goes downhill as a scared child (who shouldn't have an ASSAULT rifle) does not know how to act.
skinny
This article (posted earlier) does a better job at telling a more balanced story than the video on background.
https://www.newyorker.com/magazine/2021/07/05/kyle-rittenhouse-american-vigilante