You can't generically just "lose" a move; you can do some three-move wiggles but you'd be relying on your opponent cooperating with you.

Huh? Black and White are not symmetrical, so it's not a matter of chucking a turn somewhere somehow.

They are symmetrical once you mirror.

Nope, it's pretty basic theory that 1 turn advantage changes this symmetry completely. Take a chess board and try it yourself.

That's why you need to lose exactly one move to make it symmetric. Like my original comment said.

And we don't want symmetry on one board, but between two boards.

Still no, you cannot lose a move in the opening. There is no "pass" move in chess. In fact any initial move no matter how wasteful you try to make it, will very soon alter the game. Even rook pawn a3 or h3 will soon have an influence in the game and cannot be ignored. It's very hard to craft the equivalent of a lost move in the early game - say, use an extra move with the bishop or something like that - and it's virtually impossible without the collaboration of the opponent.

Try it yourself vs a few instances of your favourite chess software or just here http://www.chess.com/play/computer (requires Java). Open a few instances and see how can you chuck away a move.