There are two books. What are the differences between Example 1 and Example 2?
Example 1
One of the books is a must-read.
Example 2
Either of the books is a must-read.
There are two books. What are the differences between Example 1 and Example 2?
Example 1
One of the books is a must-read.
Example 2
Either of the books is a must-read.
One book is a "must-read" in example 1.
Two books are a "must-read" in example 2.
Example 1 implies that only one out of the total number of books is a "must-read".
In Example 2, both books are considered a "must-read". You could choose either of the two books and would always end up with a "must-read".
For example 1: one of the books is boring/unsuitable/irrelevant but the statement does not distinguish which book is the "must read" and which is the other.
For example 2: both books are "must reads", but reading just one of them is sufficient. The statement does not guide as to which is best, leaving the choice to the reader.
I agree that if you say "one of the books is a must-read," then what you mean is quite literally that one of them is a must-read, almost certainly with the implication that the other isn't.
However, I don't think the second example is a good solution either. Its meaning is at best inelegantly expressed (if not entirely self-contradictory). In fact, the only way I can squeeze a modicum of sense out of the sentence is by concluding that neither of the books is a must-read, since it appears you need not read one of them as long as you read the other.
I'd express that intention very differently (dispensing with the expression "must-read" altogether):
e.g.: "You'll need to read one or other [of the two books]."