Chess.com not working according the rules of chess

As I understand it, it is impossible to make an illegal move playing here (and
on other sites too). Isn't this against the rules of chess? It should be the
responsibility of the player to call out an illegal move.

Let the players make whatever move they fancy and have a button for illegal
move check. When a player suspects an illegal move he presses the button and the
software checks the legality of the move. Two wrongs, either two illegal moves
or two wrong calls or one of each loses the game.

Newbies would lose some games at the beginning but they would learn the rules
this way too.

What rule is it that you are seeking to enforce? I think there is no such rule- encouraging players to move however they please. It was only the custom.

/ So when self-driving cars come along, you will complain that student drivers won't crash any more?

You misunderstand me.
The background is that when you are not playing online there are no software
that checks the legality of moves. It is up to the players to do it. There are
rules for this sort of thing in the FIDE rulebook. I am proposing that
chess.com (and other sites) behave as face to face chess do.
I am in no way encouraging players to move however they please. I wrote that
two wrong moves would lose the game if the opponent calls them. If there is a
concern that some players would publish nonsense games where no player would
call out an illegal move make the software have both players lose the game,
with normal rating loss, after both make two illegal moves.
Of course, self-driving cars have nothing to do with this. Every idea should
be judged by it's own merit.

I can see this being incredibly confusing for people trying to learn chess or just starting to try speed chess. This should not be the default, but it might be nice to have this available as an optional game-type.

Checking for legality has almost always been one the functions of any worthwhile chess software. I would think online, having the software that checks the legality of a move, then ignores the legality of the move but allows for a dispute concerning the move played would not only be extremely complex and confusing but would make the game less, not more.  The same logic would dictate that if we click on a piece, we'd had to move that piece per the touch rule  The fact is OTB and online aren't the same in all aspects, nor, in my opinion, should they be or you'd be tapping a clock button each time you moved.  

The problem with having illegal moves is that it can be so easily misused in fast time controls (especially bullet).

Have just a rook compared to your opponent's two? Just make a few illegal moves and in the time it takes your opponent to notice and claim them, the game is yours.....

Admittedly the above situation is a slight exaggeration but that is exactly what could end up happening in bullet in a time scramble. Furthermore, an illegal move would have to be punished in some way and for most reasonably strong players (>1500) illegal moves are quite rare and only the result of mouse slips. To me it seems quite unfair to punish so many mouse slips just to punish the few intentional illegal moves that actually would occur.

It would be nice if more people would write if they think software should
make it impossible to make illegal moves.

@batgirl
The touchmove and clock idea are independent from each other and my
suggestion, and may be implemented independently if desired.

@hashtag_whales
Wouldn't it be less desirable to try to bluff in bullet? To click on a button
for legality check can't possibly take longer time than making a move. And
after the first offence the opponent gains two minutes on the clock, which
would be a huge advantage in bullet. After the second, the game would be lost.
(The two minute punishment is from the FIDE rules.)

If you want an OTB experience, play OTB. Many people play online for fun. This just makes it more frustrating. The rules you're stating apply mostly to tournaments, not casual.

Since the crux of your argument is that online chess should mimic OTB chess, ["I am proposing that chess.com (and other sites) behave as face to face chess do."] both these conditions would be required, not peripheral, if one were to follow your reasoning.  If you don't think either of these actions are necessary, then the basis for your argument seems faulty to me. 

Are you talking about "en passant"?

@batgirl
As you can implement each of these things independently of each other and
discuss the value of each without that valuation having any influence of the
valuation of the others they are independent.

Anyone in this universe have all the right to think it should be a package
deal. Personally I think that all independent features, wherever they would be
implemented, should be independently reviewed.

As anyone can see, I have not said anything about whether or not your
suggestions would be good. All I wrote was that they are independent.

@ChronosGodGT
Thank you for your offer to help, but I know the rules of chess pretty well.

Either you want online chess to mimic OTB or you don't.  My point is that you don't get to cherry pick the areas to want to mimic OTB and retain your premise that you want online to be just like OTB.   For me it isn't whether these things can be implemented (none of them seem practical or necessary to me, but that's another point altogether) but that you must follow the logical implications of the original premise. 

I've already written that's fine by me to make it a package deal.

Would a solution be to keep it as it is, but have a "learning" option that tells you WHY you can't move like you want? Example:; If trying to castle through check, currently it "just won't move." An option could be to have the check light up, flash red 3x, or catch fire. A step beyond that would be a pop-up "castling through check". This would help new players learn, without illegal moves actually being made. Another option with less coding issues would be a help button. If you can't make the move you want, press the WTF button, and your opponent can help, or a tutorial, or an auto post to forums.

Your suggestion is excellent for beginners. I wanted to point out that online chess works in a different way from OTB. And I wanted players to think if that is good or not.