Missed this specific piece: Yes, you are always free to muck your hand without showing if you are conceding the pot, say because the other player voluntarily showed their (better) hand even if they could have asked for you to show first. All the discussion above about who “has” to show only applies if two or more people are in the showdown and the hand hasn’t been resolved through voluntary reveals already.
Other tidbits in the “showing of hands” area –
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You actually need to “table” your cards (face up flat on the table) to show them, not just show them casually, like waving them face out or something.
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Any cards you show to anyone should be shown to everyone (a.k.a. “show one, show all”). So, leaning over to a neighbor, showing him your busted KK with a sigh, and then mucking is technically not allowed. It’s usually tolerated if it’s rare and the vibes are good at the table, but people will invoke “show one, show all” on a player that repeatedly does this.
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You may come across a rare instance where a player who was in the hand at any point insists on seeing the hole cards of a player that would not normally need to show. For instance, Player A bets on the river; Player B calls; Player A shows a monster hand; Player A folds; Player C (who folded ages ago) says, “I want to see that hand”, and the dealer reveals Player A’s cards before sliding them into the muck. The original principle of this rule is to prevent collusion, but I’ve only ever seen it invoked by some jaded card-dead player who wants to regain some sense of free will. Not all card rooms have the rule, but it’s considered very poor etiquette to use it, so don’t do this (but also don’t be surprised if it does happen on rare occasion.)
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“Cards speak”. When cards are tabled, it doesn’t matter what value of hand a player thinks they have. The cards are the cards, and a proper reading of the hand’s value always applies. So, if someone flips over cards and says, “Top pair!” and someone else says, “Bro, you have a straight,” a subsequent loser to that straight shouldn’t be upset by the hand value being pointed out, as it’s the fair outcome regardless (and if it’s in a card room with a dealer, it would have been pointed out anyway.)
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If all players are all-in, some tables may require all hands to be shown even prior to dealing out the rest of the board. This is more common in tournaments and less common in cash games.