The final words in the story best summarise why Jerry did not challenge his mother's instruction that he should not go swimming any more that day:
It was no longer of the least importance to go to the bay.
The reason for this is that he had just gone through an extremely difficult trial that he had put himself through. He had almost lost his life and had to overcome his fear and tremendous difficulties to complete the arduous task that he had set himself.
The reason why Jerry had imposed this amazingly strenuous task on himself was that he had to regain the dignity he lost when a number of older boys humiliated him when they swam away from him during his visit to a wild bay. They had been diving into the water and swimming through an underwater tunnel running through a rock.
Jerry's attempts at diving were quite pathetic because the salt water stung his eyes. He could see the boys' disapproval when he tried to prove his worth by performing some foolish tricks and he felt ashamed. His attempt at speaking their language was also ignored and they later left him alone. Their rejection so humiliated him that he cried copiously.
It became imperative for Jerry to prove himself the boys' equal and he asked his mother to buy him a pair of swimming goggles. He returned to the rocks and persistently tried swimming through the tunnel. Two days before the end of their vacation, he decided that he had to succeed on that day. There would be no other. In the process, he had to overcome tremendous obstacles: he was afraid, his nose had been bleeding and the tunnel was narrow, but he refused to give up.
Jerry had taken an amazing risk, but his persistence paid off. He finally got through the tunnel, and almost lost consciousness during his struggle. When he finally got through, his eyes and nose were bleeding, but he was generally fine. His achievement was a source of tremendous pride for him. He had proven that he was the boys' equal and that their rejection had been an oversight.
With his self-respect restored, Jerry had nothing more to prove and going back to the beach to swim was, therefore, not an issue any more.
In Doris Lessing's "Through the Tunnel" the conflicting forces of the authority of Jerry's mother and her son's freedom move the plot throughout the story. However, after Jerry practices holding his breath and finally succeeds in swimming through the underwater tunnel he completes his rite of passage and feels the equal of the older boys who have shunned him earlier. Consequently,
[H]e did not want them. He wanted nothing but to get back home and lie down.
When Jerry returns home, he is simply ready to rest after his exhausting venture. But, he does want to inform his mother of his accomplishment; and, when she urges him to not overdo his swimming challenges, 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.
Jerry no long has anything to prove because he knows that he is capable of doing whatever the older boys do, and he feels he has matured now and is no longer a young boy. Therefore, he acquiesces to his mother's wishes which do not carry the importance he once attached to them.