A Mexican standoff is most precisely a confrontation between three opponents, facing each other. The tactics for such a confrontation are substantially different than for a duel with only two opponents, where the first to shoot has the advantage. In a confrontation with three mutually hostile participants, the first to shoot is at a tactical disadvantage. If opponent A shoots opponent B, then while so occupied, opponent C can shoot A, thus winning the conflict. Since it is the second opponent to shoot that has the advantage, no one wants to go first.
3 dudes aiming at each other-A aims at B, B aims at C, C aims at A.