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How each layer of a neural net is responsible for one feature

Through my study of neural networks I came across the idea of that each layer of a neural network is responsible for recognizing one feature of the input data. For example, if we build a neural network that classifies cars, buses, vans and bicycles, a layer will be responsible to recognize the tires, another one will responsible to recognize the size of the vehicle. The question is, why is this true? i.e. each layer appears to perform similar to the others and there is no special design for each one. Is there anyway to assign each layer a specific feature or it is done implicitly?