2 players in the hand. Does a player have to show, expose his/her hand if, at the completion of the river and final betting the calling player makes the mistake of exposing their hand first. The called player tired to muck and a heated discussion insued. The issue was resolved poorly but I am curious as to whether the player who errored in exposing early as well as other players at the table have the right to see the hand that is called no matter what the sequence is in exposing hands. This deals with tells, strategy and reading the opponents style.
The losing player is not required to expose his hand unless other players ask to see it. If the other players ask to see the hand, he is required to open it.
Some card rooms might have different rules, especially at home games. But this is what Robert's Rules of Poker says:
8) If everyone checks (or is all-in) on the final betting round, the player who acted first is the first to show the hand. If there is wagering on the final betting round, the last player to take aggressive action by a bet or raise is the first to show the hand. In order to speed up the game, a player holding a probable winner is encouraged to show the hand without delay. If there are one or more side pots (because someone is all-in), players are asked to aid in determining the pot winner by not showing their cards until a pot they are in is being settled. A player may opt to throw his hand away after all the betting for the deal is over, rather than compete to win the pot. However, the other players do not lose the right to request the hand be shown if he does so.
However you should note that it is poor etiquette to request to see a losing player's hand. This rule is in place not to satisfy your curiosity, but to empower the players to police the games and identify cheaters and collusion. Don't be that guy.