Usually, when the wrong way of saying something catches on so popularly that we throw our hands up in surrender, it's the relatively uneducated who made it thus. But in this instance, it's the opposite; it's those who think pretty highly of themselves and their linguistic abilities who run around saying, "Aren't I?"*Â
I can't even watch one hour of BBC television without some Cambridge or Oxford graduate asking the question without the slightest hesitation or sense of impropriety.
For me the problem is two-fold.
On the face of it, it appears that we now allow the be verb are to be used with the pronoun I. But we don't. That would violate the inviolable law of subject-verb agreement.** It's confusing. For example, are I not allowed to say, "Are I not beautiful?" without the contraction, or are I only permitted to use are with I as a contraction, i.e., "Aren't I beautiful?"
It's classist. We already had a negative be-verb contraction for the pronoun I: ain't. But "uneducated" people were using it wrong, so it got locked up in the Cage with Lucifer, banished forever from polite society. And now we have "educated" people slinging around the absolutely wrong be verb, and we clean out the pool house and invite it to stay. Ugh.
Consider this: Use "Am I not?" instead.
"Am I not" pairs the right be verb with the pronoun I and is faithful to the classic PUG doctrine of subject-verb agreement. I also believe that "Am I not?" would go down cool and easy with the snootery.
Besides, like most bukis, this one carries the Master Squid Hey, it's never wrong guarantee.
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* Merriam-Webster considers the phrase acceptable (actually, "accepted") and offers a good summary of the issue.** We can change that, you know? Many European languages made their second-person plural pronoun singular and made the accompanying plural be verb singular to facilitate the change, e.g., "you are" in English.