He has always insisted on his being called Dr Turner instead of Mr Turner.

老师,为何例句中,用his而不是him?

1.句中的his也可以换用him,his being called Dr Turner instead of Mr Turner是动名词短语作has insisted on的宾语,his(或him)是动名词的逻辑主语。
2. instead of“代替;而不”是短语介词(成语介词或复合介词),等于in place of或rather than。其后一般接名词或代词。若后接与谓语对应的动词,一般用动名词,不需要不定式。常用作状语表示“择比”。比如:

Will you go to the meeting instead of me? 你代替我去开会怎么样?

Lets play cards instead of watching television. 咱们玩纸牌吧,别看电视了。

Instead of Graham, it was Peter who moved in. 搬进去的不是格雷厄姆, 而是彼得。

▲ instead of常具备连词的性质,可以连接两个相同的语法成分(如你问题中的Dr Turner instead of Mr Turner)。比如:
Id like some tea instead of coffee. 我想要茶而不是咖啡。
He drove steadly instead of slowly. 他开车开得稳而不是慢。
We went thereon foot instead of by bus. 大家没乘公共汽车,而是步行去的。

He went there to gain money instead of to spend money. 他到那儿去是为了赚钱而不是烧钱的。