Should the word history be capitalized when referring to History teacher?

No, "history" should not be capitalized when referring to a History teacher.

Here's why:

* "History" as a subject: When referring to the academic discipline, "history" is not capitalized.

* "History" as a descriptor: When used as an adjective to describe the teacher's subject area, "history" is still not capitalized.

Correct:

* I have a History teacher.

* She's the best History teacher I've ever had.

* My History teacher is very knowledgeable.

Incorrect:

* I have a History Teacher.

* She's the best History Teacher I've ever had.

* My History Teacher is very knowledgeable.