English, as a living language, slowly evolves over time. It used to be primarily a Germanic language – including following Germanic capitalization rules (such as capitalizing all nouns). See, for example, the U.S. Declaration of Independence, which has a lot of capitalization that looks strange today. In the past couple of centuries, French, and more recently Spanish, have heavily influenced English vocabulary, and in this case, grammar. In French and Spanish capitalization is much sparser – not even the days of the week are capitalized, for example. Only the first letter in a title is capitalized (as in the title of this thread, which, 20 years ago, would probably have been written as "Priesthood Offices on Certificates").
The good thing about a living language is that it evolves slowly – so we probably have another 50 years before it will become incorrect to write "High Priest." Right now we're in a time where either is correct, and it seems that the Church (at least since the 2010 Handbook) is leaning towards less capitalization.
Samuel Bradshaw • If you desire to serve God, you are called to the work.