Beyoncé's "Best Thing I Never Had" is a song about her saying good riddance to her boyfriend. It has some cleverly engineered but contradictory sounding lyrics:
Sentences 1 and 2 use exactly the same phrase "the best thing never had" to mean directly opposing things for You and I. While sentences 2 and 3 seem to flatly contradict each other, but mean the same thing. How come?
Let's analyse the sentences and see how they work. To make it simpler, I'll refer to the singer as B (for Beyoncé) and him as C.
Starting with sentences 1 and 2, the trick lies with the word "best" and how its scope can be stretched in two ways, making the phrase ambiguous.
Sentence 2 ("I will always be the best thing you never had") has the simpler interpretation. B (Beyoncé) states that she is the best thing. The word "best" is tightly bound to the word "thing" - it has a very restricted scope. So "best" here can mean its usual 'highest valued'. And then the "you never had" is an extra bit of information that states that C (he) has never had B. The upshot is that B is the best thing. Here it is a bit more formally:
[B is a thing ∧ ∀x[[x is a thing ∧ ¬x = B] → B has higher value than x] ∧ ¬C had B ]
In sentence 1 ("You turned out to be the best thing I never had"), the not-having is being done by B. The scope of the word "best" can include the "never" and then its negation affects the interpretation of "best". So "best" here can mean the 'best to not have'. The best thing to not have, from her point of view, is the lowest-valued thing. So, loosely speaking, C is the worst thing. This is the key to the seemingly misworded song title.
[C is a thing ∧ ∀x[[x is a thing ∧ ¬B had x ∧ ¬x = C] → C has lower value than x] ]
Sentence 3 ("I will never be the best thing you never had") is interpreted in the same way as sentence 1 (with the parties exchanged) and then negated by the initial "never", and not as simply a negation of sentence 2 despite the syntactic similarity. C is doing the not-having and from C's point of view, the best thing to not have is the lowest-valued thing. So here "the best thing you never had" says that B is the lowest-value thing that C has never had. The "I will never be" inverts this to mean B is the highest-value thing that C has never had (and adds that this state will be maintained as long as B is around). So, again roughly speaking, B is the best thing.
¬[B is a thing ∧ ∀x[[x is a thing ∧ ¬C had x ∧ ¬x = B] → B has lower value than x] ]
Of course, our dual interpretation of these ambiguous sentences is made in the context of the rest of the lyrics. In isolation, we could interpret them in other ways and have one of the following:
Using the open world assumption, these 'best to not have things' will never do. Neither party can know the value of all the things they've never had, so the superlatives are moot.