What’s wrong with saying “Have a nice day”?

I once read the book Class: A Guide Through the American Status System by Paul Fussell. There, he mentioned that saying “Have a nice day” was a faux pas, without elaborating why.

I’m not American, this is way too subtle for me and Google did not help. Therefore, I’ll ask here: what is wrong with this phrase, and what should I say instead in situations where I would use it (like for example parting with a person)?

I’m not making this up, either: look at the first paragraph.

There's nothing wrong with "Have a nice day" in itself.

Paul Fussell is simply engaging in a bit of elitist, curmudgeonly nose-holding about the hoi polloi, whose membership in the great unwashed is marked by their use of the phrase, "Have a nice day." This excerpt from the book is telling:

Dear Sir,

My banker embarrasses me terribly by saying at the end of the transaction, "Have a nice day." I don't know what I'm supposed to say back. Can you help?

Sincere

Dear Sincere:

The best response to "Have a nice day," I think, is one devised by a British friend of mine. He says: "Thank you, but I have other plans." Perfectly polite, and yet it leaves no doubt that you are not in that person's social class.

But to finish answering your question, the most generally applicable English phrase to use when parting is, "Good-bye."

The phrase "have a nice day" is commonly heard coming from the mouths of those in service positions (source: I work at a fast food restaurant). Since he makes note that the middle class is large and earns little, and is largely uneducated, he may assume that these uneducated folk will be filling large numbers of low-paying service jobs, which will increase the usage of "have a nice day," a phrase that he loathes.

Have a nice day, by the way.