Cars steer by adjusting the angle of the front wheels. The back wheels are always aligned with the front of the car. When you back into a space, you get the part of the car that can’t turn in first, and then you adjust the position of the part of the car that can turn.
If you try to pull in, you need more space because the only way to get the back wheels parallel to the curb is by driving forwards until the car completes the turn.
I used to mow the rough at a golf course, and my mower was the opposite of a car – the front wheels were rigid, the back wheel was what turned, and that was to make it easier to drive the mower **forward** into really tight spaces (like in between bunkers and the green)
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