I think it is mirror symmetric, and I think the confusion stems from "left for white and right for black". I believe the author means "files earlier in the alphabet" for both, and the different handedness comes from players generally sitting on opposite sides of the board.
Hmm... Maybe. Now that you mention it, it is ambiguous whether "left" and "right" in this context (e.g., "for black") means from that player's perspective. I still think that's probably what the author meant, but it is not clear. It should be phrased like "toward the A-file" for clairity.
In the starting position, remove the major pieces. Treat the pawn row as a cellophane film, and pull it tight around the king, "sticking" the e pawn where it is. The d and f pawns also get stuck where they are, the c pawn gets pulled down into d1, the b pawn further pulled to d0 (offboard), and the a pawn down and around into e0. Similarly for the right half of the pawns, and now the position of the pawn relative to the king is the same direction that that rank's pawn grants power to the king. I do think this is a good mnemonic; anybody good at a quick animation? :P
Ah! Thank you! This makes sense :) You don't need to remember which files are which directions because there is a pattern to it. I wasn't thinking of an animation, but even before your comment I was picturing diagrams with the kings surrounded by file letters to indicate which file's pawns corresponded to which directions.
Hmm... Maybe. Now that you mention it, it is ambiguous whether "left" and "right" in this context (e.g., "for black") means from that player's perspective. I still think that's probably what the author meant, but it is not clear. It should be phrased like "toward the A-file" for clairity.
Ah! Thank you! This makes sense :) You don't need to remember which files are which directions because there is a pattern to it. I wasn't thinking of an animation, but even before your comment I was picturing diagrams with the kings surrounded by file letters to indicate which file's pawns corresponded to which directions.