"The office of the President" or "the office of President"?

Solution 1:

The office of the President in the Amendment means the presidency which is defined as:

the job of a president or the period of time when a person is president

Note: the is not used before president even though it is not capitalized in the definition.

The reason to use the definite article the is to show that the President is unique or a particular member of its class as indicated in Merriam-Webster's definition:

The is used as a function word to indicate that a following noun or noun equivalent is a unique or a particular member of its class: the President, the Lord

However, when someone is elected to the office of the President, the noun President becomes a proper noun which doesn't require any articles before it as in:

King George, Queen Elizabeth, President Obama, Prime Minister Cameron, Prefessor Jones, Father Smith, Judge John, Sir Walter Scott, etc.

Note: There are exceptions; The Emperor Napoleon, The Czar Nicholas.

The reason we don't use the in the above examples is there is only one person who is called that way during his/her term as President, Prime Minister, Father, etc, which makes those nouns a proper noun.

When you read the Amendment, you will notice that President without the is referring to any existing President who has been elected to the Office of the President and all office of President's were used as objects of the verb hold and President's were used as objects of the preposition as.

The oath of office of the President of the United States has the following wording.

I do solemnly swear (or affirm) that I will faithfully execute the Office of President of the United States, and will to the best of my ability, preserve, protect and defend the Constitution of the United States.

The reason why there is no the in the oath is the same as the 21st Amendment. President of the United States is just one person who can have maximum 2 terms.

[Merriam-Webster, Wikipedia]

Solution 2:

Since there is only one elected (titular) 'President' at a time, the definite article is not needed. I would have omitted it everywhere, lest anyone think that the 'office' was merely referring to the room that he sits in, although that is where he goes when elected, and he certainly can't hold it in his hands.