Can a pawn capture backwards?

No. A pawn captures one square diagonally forward and nothing else, so an enemy piece sitting behind it is completely safe from it. En passant is no exception either: the capturing pawn still moves forward, onto the square the enemy pawn skipped over. A pawn that has passed something has passed it for good.

Can a knight move backwards?

Yes, in all eight directions. The knight's move is symmetrical, so wherever it has just come from it can go straight back next turn. That is why manoeuvres like Nb1-d2-f1-g3 work: the knight goes backwards to f1 to reach a better square on the kingside two moves later.

Why can pawns not move backwards?

Because the game would never end. The pawns are the only pieces that cannot retreat, which is what gives a position its shape: pawn moves are permanent decisions and pawn structures fix themselves in place. The compensation is promotion. Reach the eighth rank and the pawn becomes a queen, which is a very large prize for a very small piece.

Which chess pieces can move backwards?

Five of the six can. The king steps back one square like he steps anywhere else. The queen, the rook and the bishop retrace any line they can travel forwards, so a bishop that has gone d3-h7 can come back d3 next move if it likes. The knight can always jump back to the square it left, since its move works identically in both directions.

Only the pawn is stuck going one way.

The knight goes b1-d2-f1-g3, backwards to f1 and then out to the kingside. It is the standard Spanish route, and no pawn could ever do it.

The pawn, and only the pawn

Article 3.7 gives the pawn a forward move, a double first move, and a diagonal capture one square forward. That is the complete list. No backwards move, no sideways move, no backwards capture. Even en passant, which looks like a trick, is a forward capture onto the square the enemy pawn skipped.

So a pawn on e5 will never defend e2 again, and the square e4 it left behind is not coming back under its control. That is what people mean by a weakness: play g4 to chase a bishop and f4, h4 and the squares around your king have changed for the rest of the game, whether it worked or not. Philidor called the pawns the soul of chess in 1749, and part of what he meant was that they are the only part of the position you cannot take back.

Backwards is often the best move

Beginners almost never retreat. A piece that goes forward feels like progress and a piece that comes back feels like an admission, so they leave a bishop where it is being attacked and lose it, or push a knight further in until it drowns.

The most famous manoeuvre in opening theory is a retreat. In the Ruy Lopez, White plays 3.Bb5, gets kicked by 3…a6, retreats 4.Ba4, gets kicked again by …b5 and retreats to b3, where the bishop stares at f7 for the next thirty moves. Two backwards moves and the piece ends up better than it started. The knight tour in the same opening, Nb1-d2-f1-g3, is the diagram above.

When you cannot find a move, try looking behind you. A knight on the rim usually has a beautiful square two moves back.

What the pawn gets in return

Promotion, which is a big enough prize to justify the whole arrangement. A pawn that reaches the eighth rank turns into a queen, or a rook, a bishop, or a knight, and a game that was level becomes a king and queen mate. That is the deal: no retreat, but a crown at the end of the road. Look at any promotion puzzle and you will see how much a beginner’s pawn is really worth, and how many queens you can end up with if the pawns keep arriving.