He doesn't know how to enjoy the heron the way Sylvia does, and all he can think of to do with it is to kill it and stuff it -- to bend it to his will and make it something pretty for display, and a testament to his own prowess and skill. This is indicative of the way he treats the world, as his greeting of Sylvia's grandmother on first meeting her clearly shows: "Put me anywhere you like,' he said. 'I must be off early in the morning, before day; but I am very hungry, indeed. You can give me some milk at any rate, that's plain'" (Jewett par. 12).
In addition to this attitude and what it implies for his view and treatment of the heron, there are also other indicators regarding Sylvia's sexual awakening in the story. On her way home through the woods at the very beginning of the story, she recalls the "great red-faced boy who used to chase and frighten her" (Jewett par. 4). It is immediately thereafter that she hears the young man's whistle and tries to hide. Both of these incidents make her fear of the opposite sex quite plain. The next day, however, when she and the young man are walking the cow home through the woods together, "smiled with pleasure when they came to the place where she heard the whistle and was afraid only the night before" (Jewett par. 26). At this point in the story, Sylvia has already lost a part of her innocence, and though it has caused her no detriment experience shows that this is an irreversible trend. Growing used to the presence of the young man and even enjoying his company is a sign that Sylvia is coming out of the shell that she has built around herself in her childhood and is taking her first tentative steps towards becoming a woman.
Her decision not to give up the heron, though it torments her for many nights thereafter, reveals that she is still far too innocent, perhaps due to her age but even more likely due to a purity of spirit that is simply a part of her. This purity took a definite hit in the story, and it is rendered almost palpable by Jewett's masterful and romanticized storytelling, but it persists in one way or another nonetheless. It is the loss of innocence she experiences at whatever degree that makes this a true coming-of-age story, and a truly great short story as well.
Jewett, Sarah Orne. "A White Heron." Retrieved from the Online Archive of Nineteenth-Century Women's Writings. Ed. Glynis Carr on 3 October 2009. http://www.facstaff.bucknell.edu/gcarr/19cUSWW/SOJ/AWH.html