Have you read the TDA rules?
TDA rule # 11 says:
"All cards will be turned face up once a player is all-in and all betting action for the hand is complete. The dealer & players should insist on timely compliance with this rule."
If you're running a tournament, and, if you're using TDA rules, and, if a player asks why his hand must be shown at an all in showdown, you can say "Because the rules say so."
If a player asks why the rule is being enforced, you don't need to explain why. If you're running a tournament, and, if you don't understand why some of the rules are the way that they are, you can ask questions here. For the most part, the answers that you'll get are best guesses and/or excuses.
But the rules are really not difficult to understand if you understand the language in which the rules are written.
"All cards will be turned face up once a player is all-in and all betting action for the hand is complete. The dealer & players should insist on timely compliance with this rule."
Rules are, of course, easy to understand, but the reason I would let player C or B muck their hand is:
-1) they were still playing at the river and there was a side pot running between them
-2) showing losing hand could affect the strategy of the player who could have nothing and doesn't want to show his bluff (let's think at B who bets the turn and then check the river) and we always have to protect players for the best interest of the game.
-3) main pot should be awarded to the player with the winning hand between A and (B or C), so there's no reason to show the loosing hand between (B or C)
It's just that a lot of TD's here in Italy (and I don't know if in Europe also) sometimes consider last aggressive action on the turn and let player A muck is hand unless the winner asks to see them.
I don't let them do this, A is all-in and must show his cards. That's easy to understand lol.
Otherwise some TD's let the players with loosing hand muck.
I think that's also because we shouldn't put a lot of pressure on the players by ruling everything they do in a wrong way especially if we have novices. And I'm talking about the action between player B or C, not A.
If we should do so, game would be affected.