“Everything is not…”

I keep hearing people say everything is not… which frustrating because it is ambiguous. It could mean either

Nothing is… (for the set of all things, no thing is…)

or

Not everything is… (for the set of all things, some things are not…/not all things are…)

I have been hearing it more and more in the past few years. In fact, when you Google the phrase everything is not, you get Selena Gomez’s rendition of the Wizards of Waverly Place theme song which only further popularizes it with the youth.

Is this phrase grammatically correct/legitimate (ie, would an English teacher complain?), and if so, which is the correct meaning (if any)?

Looking in Google Ngrams, people have been using the phrase "everything is not" for the last 400 years. If you actually look at the instances, virtually all of them (except those written by logicians or Buddhist philosophers) mean "not everything is", and virtually nobody uses it to mean "nothing is". This phrase is only ambiguous for logicians. The correct meaning (if you're not a logician) is "not everything is".

Unfortunately for logicians, language is not always based on logic.

Even Shakespeare had his characters use "all is not" in this way:

All that glisters is not gold;
Often have you heard that told: —(The Merchant of Venice)

All have not offended; —(Timon of Athens)

He did not mean "Nothing that glisters is gold" and "None have offended" by these.

In English, sentences containing both a negative and a quantifier, or a negative and a modal, or a modal and a quantifier, are ambiguous, unless some care is taken in phrasing them. If (as here) there is both a universal quantifier everything, and a negative particle not, then there will normally be two meanings:

• one with the negative inside the scope of the quantifier : (∀x)¬P(x)
• one with the negative outside the scope of the quantifier : ¬(∀x)P(x).

This is true of any sentence that contains any two logical Operators (Modals, Negatives, Quantifiers). In other words, such ambiguities are unavoidable, so you might as well relax; they're gonna be around a long time, and who needs the tsures?

In fact, virtually every possible English sentence is multiply ambiguous in print (though not nearly so much in speech, where rhythm and intonation usually distinguish nicely); but because we can figure out what's likely we happily ignore the unlikely though logically possible meanings, and go for the contextually sensible ones.

The correct grammatical (and also mathematical) meaning of the phrase is the former one:

Nothing is... (for the set of all things, no thing is...)

But unfortunately in the majority of cases people mean the latter one:

Not everything is... (for the set of all things, some things are not.../not all things are...)

I wouldn't say the phrase is ambiguous, it's just that people are used to using it incorrectly and you won't change that.

If you don't want to be misunderstood, don't use the phrase. If you want to annoy the people using it, misunderstand them.