We are presented with a very awkward relationship between the protagonist of this excellent short story and his mother as Jerry is on the threshold of adulthood and his mother struggles to work out how best to give him limited independence whilst trying to ensure his safety. Note how we see a conflict between them right at the beginning of the story when she spots Jerry looking at the "wild beach," and how "contrition" forced him to follow her to the "safe beach." Perhaps the most revealing paragraph we have that addresses their relationship comes when the author tells us some background information about the mother and Jerry:
He was an only child, eleven years old. She was a widow. She was determined to be neither possessive nor lacking in devotion. She went worrying off to her beach.
Thus we can see that the mother, as a single mother, is desperately trying to raise Jerry well by herself, and wants to try and get that balance between giving him independence whilst at the same time letting Jerry know that he is deeply loved. Thus it is that she lets him go to the "wild beach" by himself.