French books are loaded with facts, but few with explanations.
All the French grammars I know publish the list of the neuter verbs that are conjugated with the auxiliary être, but none give boys the reason why these verbs are conjugated with être and not with avoir. Boys learn this list of verbs and forget it, and you know little of boys' nature if you imagine that they will consult their grammar at every turn. Some do, to be sure, but how many?
I do not know of one French grammar that tells students that neuter verbs, which express a state as well as an action, or rather that neuter verbs which express that a state is enjoyed as soon as the action is over, are conjugated with être.
A boy will understand you, and remember what you say, if you tell him:
"As soon as you have died, you are dead. This is why the verb mourir, expressing the state of being dead, as soon as the action of dying is over, has to be conjugated with être."
"As soon as you have arrived, you are arrived."
"As soon as you have been born, you are born."
"[Therefore ] all these verbs arriver, naître, venir, sortir, partir, etc., are conjugated with être."
"By this reasoning, with courir (to run) you get an absurdity. 'As soon as you have run you are run' is an absurdity. Therefore courir, expressing only an action, not a state, takes avoir."
Yes, boys will understand all that, and nothing gives them more pleasure than having their minds satisfied with a little explanatory food. I have seen rays of happy satisfaction flashing over scores of young faces as they got hold of these facts.