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I would infer that the cherry tree reminded Dettering of home. Once he saw it, he decided to leave. Text evidence provided below.
"Surely I can pick cherry blossom if I want to!" he replied evasively--and after a while: "I have a big orchard with cherry trees at home. When they are in blossom, from the hay loft they look like one single sheet, so white. It is just the time."
All Quiet on the Western Front