As water is to fish, so air is to man.

so在此为代词，指代前文刚说过的，即指代as从句的表语（as为从句的表语）。

water和air分别是主句和从句的主语，as和so分别是从句和主句的表语，to fish和to man分别是从句和主句的状语。

比较下面的句子：

Water is necessary/indispensable to fish. Air is necessary/indispensable to man.

二个句子的表语相同，为避免重复，用so替代表语形容词：

Water is necessary/indispensable to fish. Air is so to man.

so前置：

Water is necessary/indispensable to fish. So air is to man.

so前置可以倒装：

Water is necessary/indispensable to fish. So is air is to man.

合并二个句子为主从复合句，由于二个句子的表语相同，故用比较分句表示相同，as的使用使得比较分句表语形成空位gap:

As water is to fish, so air is to man.

As water is to fish, so is air to man.

(Just) as we sweep our rooms, so we should sweep backward ideas from our minds.

as分句为方式状语从句，so为连接性副词，在主句作连接性状语（语义上而不是语法上连接二个句子sentence或分句clause），表示“也”的意思。