Simplest explanation: Whether A aims at B or C, he will most likely miss. If he aims at B and misses, then A, B, and C are all alive for B’s turn. If A aims at C and misses, then A, B, and C are all alive for B’s turn—the same conditions as before. So what matters are the situations in which A actually hits his target.

If A hits B, then C will kill him (since C has 100% accuracy).

If A hits C, then he faces a 2/3 chance that B will kill him.

Since 2/3 < 1, A is better off aiming at C.

Schematically, you can see that the “A misses” outcomes lead to the same cascade of ensuing possible events. (You don’t even need to work out the actual probabilities of the ensuing events, just that the cascade itself results whenever A misses, no matter where he’s aiming.)

So, comparing the situations when A hits his target, either he kills B and is ensured death B C (3/3), or he kills C and risks death by B (2/3). The risk of death is definitely better than certain death!