Question: I was studing how to say school subjects in mandarin and I saw this sentence:

我最喜欢的科目**有**艺术，中文和化学
(My favorite school subjects are art, chinese and chemistry)

Why the use of 有 in this sentecence?

Could I say/write: 我最喜欢的科目是**是**艺术，中文和体育

Answer: 
Both are ok.

Why the use of 有 in this sentecence? Because here the "科目" in "我最喜欢的科目" is kinda list, so we can say "我最喜欢的科目有艺术，中文和化学", there are Art, Chinese etc in the list. "有" is the same meaning of "there are"
You should know that the Chinese word 有 sometimes correspond to **there be** in English, so the case you mentioned could also be interpreted as a **there be** sentence. Take an example:

院子里**有**一棵树。  

There is a tree in the yard.

我最喜欢的科目**有**艺术、中文和化学。  

There are art, chinese, and chemistry, in (the list of) my favorite subjects.

While the Chinese word 是 sometimes correspond to **be** in English.

我最喜欢的科目是艺术、中文和化学。  

My favorite subjects are art, chinese, and chemistry.