Neither sounds awkward to me. Are you trying to contrast it to saying 'The brother encourages the child'? They mean different things. 'The brother does not discourage the child' is neutral in terms of what it says about the subject's encouraging versus discouraging of the subject. It does not state that the brother encourages the child. It merely states he does not discourage him. There is nothing awkward about that. I can see many scenarios where the sentence would be useful in real life.