Why was Bruno too embarrassed to say "I'll miss you, too," to Shmuel?
I think that there is some level of embarrassment in Bruno's inability to say what he wants to Shmuel for a couple of reasons. The first would be that Bruno has grown over the course of the narrative. To a certain extent, as a boy child, he is not necessarily as comfortable with articulating emotions. This becomes evident at this moment. Additionally, I think that there is a motif being established between both Bruno and Shmuel. The emotional power of the moment where both boys realize that their friendship is going to be interrupted, perhaps forever, is something that transcends words. Shmuel "could not find words to express his sorrow" at the very next moment when Bruno was "embarrassed to" say what was on his mind. It is a point where words are becoming secondary to action. Bruno's embarrassment illuminates this. He is embarrassed to say what he feels because action is something needed while words do not substitute for it. I think that this is another reason why he is embarrassed to say what is on his mind and what he does feel. The immediate gravitation to "exploration" and action is where Bruno moves, as opposed to simply talking about it.
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