Why do the output layer weights become word vectors in Word2Vec? [D]

I'm trying to understand the intuition behind Word2Vec training using a neural network. In Word2Vec (CBOW or Skip-gram), we often hear that the weight matrices learned during training contain the vector representations (embeddings) of words. However, I don't understand why the weights of the hidden-to-output layer (or output weight matrix) end up representing semantic features of words. Why do these weights become meaningful vector representations instead of just being parameters used to make predictions? I