你们老师的解释是有道理的。

表语形容词通常后接三种结构作为表语形容词的后置修饰语（现代语法称这种结构为形容词的补足语）：介词短语，不定式，that从句。传统语法中有人认为that从句是表语形容词的原因状语。

网友的这个句子中 be afraid后并列了A, B, C 三个补足语，A 为 of介词短语，B，C 分别为二个that从句，结构为 be afraid A, B or C. 

People are afraid of rejection, they are afraid that they will be seen as pushy, or they are afraid that they always want something.