Why Expelliarmus?
Easy, a trait Harry shared with James was not wanting to be a common murderer (also the reason why James saved Snape's life). And you don't have to kill in order to defeat your opponent (unlike what Voldemort things). Except from the sacrificial shield of love, there is no protection against Avada Kedavra, except for dodging the spell ORRRR preventing the spell is cast at all. Avada Kedravra requires a wand to be cast, so by disarming Voldemort Harry would technically disable him to use the Killing Curse, without having to kill Voldemort.
This theory also appears evidenced by the fact that Draco Malfoy used Expelliarmus by surprise on Dumbledore making him the new master of the Elder Wand in the process (although Draco never realized it), showing that Draco technically defeated Dumbledore on that moment even though Draco didn't have it in him to kill Dumbledore.
Now outside the world of magic when you see real sword fighting you can sometimes see that somebody who fights with honor will not really aim to kill their opponent, but rather to disarm them.
Now the fact that your opponent is disarmed doesn't mean they're helpless, but in Harry's case, disarming Voldemort would have been enough. Maybe Voldemort was lucky a priori incantatum happened, as nobody present there could really explain the phenomenon. If Harry successfully disarmed Voldemort, the question is how loyal his Death Eaters would have remained seeing that their "Dark Lord" was defeated (even if only disarmed) by a teenage boy.
Expelliarmus is a very useful spell in magic combat if you don't want to kill. Even when your opponent wants to kill you.
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