Are chess mating rules illogical?

Take a look at this position:

This is considered as white has mated black. But is it really logical?

In reality, white's Queen is not really protected. If black had any other piece attacking the Queen's square, they could take it with that piece and white couldn't recapture that piece with the knight. Then why it's not possible to capture the Queen with the King? The knight is pinned by black's bishop, does it really defends the Queen from being captured by black's king?

What's the logic behind that? That if King captures the Queen, then khight can take the King? But that would expose white's King in the same time and black could capture white's King with the bishop on the same move.

Logically, this can be a draw.

it's a turn based game. it's whites turn and he can't move two pieces at once.

If the knight moves, white's king would die on the following half-move. But in moving the knight, black's king dies right then. Chess isn't about whose king dies with how much of a lead, or in what situation, or anything like that; chess is purely about whose king dies first.

There's a somewhat similar situation in Go. Normally a stone cannot be played in a position where it or its group would be surrounded, and that would kill it. However, When a stone is be played in a position in which it would ordinarily be killed, but its placement surrounds and kills another group, that group dies and the attacker lives. It seems very logical to me in both cases that initiative should count for a lot.

Gatalsky, your logic is faulty. You claim that the black king should be able to expose himself to check because the knight cannot move. Yet you are happy to accept that the knight cannot move because it would expose the white king to check! Same rules apply to both sides.

Chess rules are quite clear. A piece can give check; support check; or control a square even when pinned.

I like this.

But what if the black bishop was somehow pinned?

What if that next piece pinning the bishop was also pinned?

What if there was some kind of double-pinned situation that could lead to a break-down in the logical structure of chess similar to Godel's theorem?

No, I think it's better to stick with the rules as they are and never think about this again.

Of course they are logical. If they were not, one could find an inconsistency. You just found an edge case that "feels" illogical to some people. But logic is not about gut feeling.

I know someone who made a counter-checkmate and won on time...

Whose King gets checkmated first loses the game.  When checkmate occurs, the game has ended.  Checkmate happens when a king is under check and (a) it cannot move to a square that is not under check, (2) it cannot capture the piece that is effecting the check, (3) and the check cannot be blocked. Those are chess rules. There is no such thing as a counter-checkmate, as well as there is no counter-"en passant", in chess.  Now that's what is illogical.  And ridiculous too.

"Then why is it not possible to capture the White Queen with the Black King?"  The rule is "you cannot capture with your king an opposing piece that is protected."  With any of your pieces other than your king, you can.  Those are the rules of chess. And rules are rules.  That's the reality of it.

"What's the logic behind that? That if King captures the Queen, then khight can take the King".   No, the knight will not take the King.  It won't even come to that.  As I mentioned previously, the rule is "you cannot capture with your king an opposing piece that is protected.  With any of your pieces other than your king, you can."