Sache is the matter, the thing itself. Sachlich means pertaining to the matter and nothing else.
English has no clean equivalent. Objectivity suggests neutrality of the observer. Matter-of-fact is a description of manner. Sachlich is neither — it names a discipline: keeping to the substance and out of everything around it.
A German asking you to be sachlich is not asking you to be calm. They are asking you to talk about the problem.