Fundamental misunderstanding of English.

“I am sad” – am here is a copula. It indicates a link between the subject (I) and subject-complement (sad). In this case, it’s saying “subject (I) has property (sad).” It does not equate the subject and subject-complement.

Not all languages work like this. In Mandarin for instance, 我是伤心* (wǒ (I) shì (am) shāngxīn (sad)*) would be seen as grammatically incorrect or at least weird. This would literally mean “I am sad” (adjectives in Mandarin operate as stative verbs, so the correct way to say this is without a copula – i.e. 我很伤心 (wǒ (I) hěn (~quite/~very) shāngxīn (sad)). (You could drop the 很 (quite), and just say 我伤心, but the connotation in this case is that you’re setting up for a juxtaposition, e.g. “I’m sad, you’re not sad.”))