Answer and Explanation:
The issue here is that the subject is not really "athletes". Let's look at the sentence more closely:
"Each of the Olympic athletes has been training for months, even years."
The subject is "each", which is a singular word. Even if the word that follows it is plural, the verb will still be in its singular form because of "each". Take a look at the example below:
- Each of the flowers has its own particular scent.
Even though "flowers" is a plural noun, the verb "has" is singular because of "each", just like in the sentence in your question.
If we removed the word "each", then the subject would be "athletes", and the verb would be plural:
- The Olympic athletes have been training for months.