It isn't impossible, it is just arbitrary. The whole reason we can have this huge thread about different names for directions is that they is just arbitrary labels, with groups of people having a consensus on what word to use.
BTW, If you really must explain it without just saying it is arbitrary, you can talk about clockwise vs. counterclockwise... which came from sundials, which came from the direction our shadows move as the sun moves. In a similar vein, Left goes against the shadows, Right follows the shadows.
Shadows come from the rotation of the earth, not its orbit. But you are still correct - if the earth suddenly started having inconsistency in the direction it spins, that explanation would fall apart.
BTW, If you really must explain it without just saying it is arbitrary, you can talk about clockwise vs. counterclockwise... which came from sundials, which came from the direction our shadows move as the sun moves. In a similar vein, Left goes against the shadows, Right follows the shadows.