The en passant rule causes problems to beginners

Some time around the 15th century, a new rule was added to chess: A pawn in its initial position (ie. 2nd rank if white, 7th rank if black) can advance one or two squares. Previously it could only advance one square. This change was made to allow a game to develop faster.

This new rule added one negative side-effect, though: It allows a white pawn to evade capture by an black pawn that's on the 4th rank, in an adjacent file (and vice-versa with a black pawn evading capture by a white pawn on the 5th rank), by advancing two squares. In order to combat this, an additional rule was added: The so-called en passant rule. In this situation, during the next move the pawn on the 4th rank (5th if reversed situation) is allowed to capture that pawn that just advanced as if it had advanced only one square. (This is the only situation in chess where capturing doesn't put the capturing piece on the same square as the captured one.)

The en passant rule feels a bit of a kludge, or a rule patch. It introduces a type of capture that's completely unique, and unlike any other capture in the game. It also is unusual in that the option to make this capture is only temporary, which is also quite unique, and unlike any of the other rules of the game (with castling rights being the only other rule that somewhat resembles this.) The fact that it was introduced to "fix" a problem in another recently-introduced rule makes it feel even more of a kludge.

It's also a relatively obscure rule for beginners. A surprising amount of beginner players have actually never heard of this rule, nor know of its existence. If somebody makes the move against them, they will often call foul, and even accuse the other player of cheating. If they are playing against a computer, and the computer makes the move, they often think that it's a bug in the program (or that the program is cheating somehow).

Sometimes even after they have been explained the rule, some such players keep feeling like it's somehow "cheating", or "unfair", or doesn't make much sense. I once read a comment by someone who seriously thought that this rule wasn't actually part of "normal" chess, that nobody actually uses it, and that computers using it is just semi-cheating, and that computer games should have an option to turn the rule off, like in "real" games of chess. (Apparently this guy had always played chess with people who agreed that the rule shouldn't be used, and got somehow the impression that it's so everywhere with everybody, or at least most people.)

The en passant rule, however, adds a surprising amount of tactical depth to the game. It doesn't happen very often, but when it does, it can be quite powerful. Just the threat of en passant capture can affect the tactics of the situation significantly (even if the capture itself never actualizes). The people who originally came up with the rule in the 15th century might not have been aware of how tactically deep the rule is, and thus it might be serendipitous, but it really adds a lot to the game.

Just having a pawn on the 5th rank (or 4th if playing black), if well protected, and depending on the situation, can be a great asset, precisely because it might be stopping both opponent pawns in the adjacent files from advancing.

One of my own games had this kind of situation (I'm not especially strong, just about 1450 elo on chess.com, but I still like this situation as illustrative):

That pawn on e5 had been a thorn in my opponent's side for the majority of the game, hindering the advancement of the d-pawn. This position is still relatively even, even though I'm now sure to capture the d-pawn. My opponent, perhaps because of time pressure or just weakness, tried desperately to save it, and advanced it two squares, no doubt hoping that I didn't know about en passant, or didn't notice the possibility.

Of course I did notice. Advancing the d-pawn is a bad mistake, and I proceeded to easily win the game with my two connected passed pawns.