Question

it's generally believed that teaching is as much an art as it is a science 如何正确分析其语法结构，

Answer 1

it's generally believed that teaching is as much an art as it is a science.
1、【that teaching is as much an art as it is a science】主语从句（后置），it是形式主语。
2、as much an art【 as it is a science 】比较状语从句作much的程度状语。
3、【试译：】人们普遍认为，教学是一门科学，更是一门艺术。

Answer 2

人们普遍相信教学和科学一样是一门艺术。
as...as...中间可以接adj./adv.的原行，也可以接名词，结构如下：as + much+a/an+n.(可数名词单数)+as...

Answer 3

it做形式主语，that主语从句teaching是主语从句的主语，里面含有一个as..as 句型结构
人们通常认为教学是像艺术一样的一门科学。