Here's why:
* Seasons are not capitalized: Spring, summer, fall (or autumn), and winter are not proper nouns and therefore are not capitalized.
* "Term" is a generic word: It's not a specific name or title.
Therefore, "Spring Term" should be written as "spring term."
However, there might be specific contexts where you would capitalize "Spring Term":
* If it's part of a formal name: For example, "The Spring Term at Oxford University."
* If it's being used as a title: For example, "Spring Term Report."
But in general usage, "spring term" is the correct capitalization.