That question is kind of moot. It's like asking why can a pawn capture en passant? And only on the first turn the opportunity is available?
I suppose, for my 2-cents, castling out of check is not allowed possibly because you theoretically could castle out of a double check? Or a checkmate? Maybe?
I understand the en passant capture was created to provide more response options under the rule allowing pawns to move forward two squares on their first move. The reason en passant is only available on the first oppurtunity is because the two square opening move is available only on a pawn's first move. It's a trade off. It also prevents a pawn from capturing two pieces at once (a pawn en passant, and whatever piece was stupidly placed into the square it passed over). Back to the question at hand though, why not castle out of a double check? It's a king move and therefore no different from simply moving a king over a square and out of danger. As for "castling out of check mate", if there was a way out, it's not mate.
I think the origin of the rule goes back to the very origin of modern castling. Under the older rules, the King could move as a Knight once in a game, but many regions had their own variations of when that was allowed. Castling standardized the rules, and was quickly adopted by the chessplaying world.
Since all those who codified the rule are long dead and there is no record of their debates on the matter, we are left to speculate as to the reasons for the particulars. I suspect it had something to do with reconciling the old conflicts, and since castling is the only move which allows two pieces to move at once, the conditions were meant to be strict - and not being in check was one of them.
Whatever the reason, it's the rule, and it's not about to change, so we must live with it.
Never said it should change. It's bad enough as it is when I think Ive got my opponent in checkmate and hes able to get out of it because Ive overlooked something. I can't imagine how much it would suck for one's opponent to be able to interpose one of the most powerful pieces on the board with his king and immediately be on the counter attack; rather than having to waste a turn evacuating the king.
Im sorry if this has already been asked before, but a search failed to return any relevant results. Anyway, I was wondering why it is illegal to castle out of check? I understand why the king can't pass over or end up on a square that would place him in check, but why is this the only manuever that is absolutely illegal for removing the king from danger?