Hello. Here are some feelings of mine about the two sentences. 我是老师: Very common word. To describe a fact. I am a teacher. 我就是老师: Two possible suitations. The one is "I am no one/nothing but a teacher", in a strong feeling. The another is to confirm people's queries/asking about your profession, like someone asks you "are you a teacher", you would to say "yes, I am totally a teacher". There is a total agreement or claim in this word.

If someone said "I'm looking for a teacher", and a second person, a teacher, replied "Well, *I'm* a teacher!", the second sentence with 就 carries this emphasis.

我就是老师 sounds more like “ I am the teacher” , to tell someone you are the one. 我是老师 simply means “I am a teacher”, to tell someone your occupation

well…for me the first sentence is very common. More like an introduction. The second sentence always contains some special emotions in it. Emphasize“ just and teacher.” 第一句话比较日常，第二句就偏向有感情，强调了“就是”之后的词。

就has two meaning. One is to emphasize the item following with it, like 老师 in this sentence. The other meaning is “only, or just”. I am just a teacher. But in the meaning it always follows with the phrase “而已”。 我就是老师而已。我就是学生而已。