___nothing to talk about,he said good-bye and went out of the room

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正确答案是：A
【解析】：
这里是独立主格做原因状语，等于：
Because there was nothing to talk about,he said good-bye and went out of the room.
there 是逻辑主语，因为从句的主语和主句的主语不一致，主句的主语不是动作的发出者。
【翻译】：因为没什么好说的，他说了声“再见”，然后走出了房间。
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There　being　nothing　to　＾这里是独立主格做状语，there这里是逻辑主语，he是主语
没有什么好说的，他说了再见就离开了房间

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A
相当于：
Because there was nothing to talk about, he said...
there being...属于独立主格结构，there相当于这个结构的逻辑主语。
不能用being，因为这句话的主语是he，不能说：He was nothing to talk about...
又如：
There being no one to help me, I had to do it all alone.
因为没有人帮助我，我不得不独立完成这项工作。