The umbrella is a symbol of protection. It begins in the boy's hands and ends in the girl's. At first he is reluctant to share it with her, though he wants to -- his shyness does not allow him to be so bold. She simply wants to share in the holding of the umbrella with him -- because it is his and he is holding it. By the end of the story, she is holding the umbrella, and she cannot bring herself to return it. Her taking it suggests to the boy that now they are united -- she can share in the protection the umbrella affords against the weather. In this sense, the umbrella becomes a symbol of marriage -- which is a kind of institution that offers protection to two people against the inclemency of time and space. Her nature causes her to want to be close to the boy -- to support him in a sense. His nature causes him to want to provide for her and also to draw her near. Their shy natures prevented them from doing so, but Fate, in a sense, prompted them to act out their affection by forcing them apart. Unfortunately, it is too late for their affections to amount to anything -- for how can they build on them if they are apart? Yet because the affection is real and strong, they make a memento of it -- and in doing so they overcome their shyness. He touches her. She takes the umbrella.

But the story is not over. As they walk homeward, he cannot bring himself to offer to hold the umbrella. His shyness returns -- despite his earlier solicitude. Her boldness in taking the umbrella is actually a sign that she belongs to him. The act is a natural one -- and in a sense they do belong to one another now. The boy has imagined embracing her naked after touching her. And she has accepted his solicitude and now sees his umbrella as...

It is only a moment that we are given to view their relationship -- barely a glimpse -- but in that glimpse we are reminded that nature is always changing us, and that we too are impermanent creatures. This idea is ironically expressed through the action of the photographer who steals a snapshot of the two together, trapping them in a moment of time as they themselves move forward in time -- and on a new path that was not open to them before: a path of adulthood.
The reason the two now feel like they have become adults is they have developed a sense of otherness. Their instincts may still be childlike, but their awareness has matured. Also, their sense of otherness unites them in a sense of togetherness -- which makes the story even sadder because it is a story about two children parting.

The theme is also about growing up. The two start out as children, but by the end of the story their marriage and old-age is foreshadowed by the one affectionate action of the girl as she stands waiting out in the rain for the boy, his umbrella in her hand. Here is where the catharsis lies -- in the exchange.

In conclusion, "The Umbrella" awakens many themes about childhood affection, and through them gives a brief glimpse into the world of adulthood, which rests upon childhood lessons like faith rests upon reason. The reality of the affection is what enables the children to overcome their childish shyness -- to an extent -- and become like adults.