Key to understanding this short story is identifying that the key theme is all about the coming of age of Jerry and his transition from the state of child to adult, as demonstrated symbolically by his self-imposed initiation ritual of going through the tunnel.
It is clear from the first few paragraphs that this story concerns a boy who is getting to the age when he needs to break free from his mother's care. Note what the mother says to herself after letting him go to the "wild beach" by himself:
She was thinking, Of course he's old enough to be safe without me. Have I been keeping him too close? He mustn't feel he ought to be with me. I must be careful.
The rest of the story marks Jerry's struggle to assert himself and prove himself to be an adult through the trial of going through the tunnel. To me, after he has succeeded, the last paragraph is very interesting:
She was ready for a battle of wills, but he gave in at once. It was no longer of the least importance to go to the bay.
Now that Jerry has succeeded in showing he can go through the tunnel, he has moved past that sign or stage of proving he is an adult and thus does not need to assert his independence on this point.
Therefore the theme of the story concerns one boy's efforts to show to himself that he is an adult and no longer a child by accomplishing the dangerous task of going through the tunnel.