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Why is a “long put” called long if you have a higher net position if the price decreases?
Long here does not mean you wish for the underlying stock to increase in value, in fact, as the chart shows, just the opposite is true.  "Long means you bought the derivative, and you own the option. The guy that sold it to you is at your mercy, he is short the put, and it's your decision to put the stock to him should it fall in value.  The value of the put itself rises with the falling stock price, you are long the put and want the put, itself, to rise in value.