When I still lived in New York, I'd occasionally hop in a taxi or rideshare and find the seatbelt buckle was turned around the wrong way. Once or twice I tried fixing it, but could never get the webbing turned around in the slot.
That's because, like a dummy I was trying to fold the webbing perpendicular to the orientation of the slot. The trick is to fold it diagonally, then pull it through:
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The larger question I have is: How the heck does this happen in the first place? I've only ever encountered this in other peoples' cars.