Learn English – Where does the term “the bag” come from

Firstly, this isn't a specifically British construction, nor is it the standard in British English. It's just a nonstandard variant that occasionally occurs in both American and British English. (More on that later below.)

As for an explanation of why it is used, I guess some people either understand the word "miss" differently than we do, or just aren't thinking clearly.

A different understanding of "miss":

"I miss not having him around" seems like a cross between "I miss him" and "I regret not having him around". The standard meaning of "I miss X" (in our context) is something like "I feel a sense of absence or loss because X used to be around and isn't any longer", thus "I miss having him around". Some people appear to be extending/inverting it to "I feel a sense or absence or loss because of X" (see the quote *"I miss that he is not around any more" in the other answer) thus for these speakers, "I miss not having him around" means "I feel a sense of something missing because of not having him around."

You can see this most clearly in the American examples:

"Do you miss not having children?"
"I feel that as an only child she may miss not having siblings later on, as an adult."

where there is talk of missing things that one never had, and

Q: Do you miss not having hands and feet?
A: Well, I've never had them.

Here the question uses "miss" in the nonstandard sense ("do you feel something missing because of not having hands and feet", a rather daft question), while the answer, having ignored the not (and the literal meaning), treats "miss" in the standard sense: I can't miss something I've never had.

As for why this different sense comes about, I guess there's a strong temptation, in phrases involving counterfactuals, to state the factual instead. (I suspect something similar was at work in the origin of "could care less", sometimes claimed to be sarcastic though it's not.)

Not thinking clearly:

This actually happens naturally in language. It's not unique to this phrase; there's a small amount of confused inversion in many phrases involving negatives:

• People frequently say "You can't fail to miss it" when they mean "you can't fail to see it" or "you can't miss it".
• They say "No one can deny that X is not the best" when they mean "No one can deny that X is the best" or "No one can claim that X is not the best"
• They say "No head injury is too trivial to ignore" when they mean "No head injury is so trivial that it can be ignored", or "No head injury is too trivial to take seriously".
• Even laywers get it wrong, and
• The non-logical usages are often far more common

I guess that, with time, "miss not" will join the list of phrases like "could care less", "doesn't know squat", and "teach you to", where a negation can be added or removed with no change in meaning. So this inverted usage of "miss" may well become standard, and it will only be considered to add to the glorious irrationalities of the English language. (In the Corpus of Historical American English, usages of "miss not" before 1968 are mostly the "correct" one, while 1968 and later has mostly the usage you asked about in the question.)

Usage patterns

Corpora indicate it may even occur more often in American English than British English, though more below.

The British National Corpus has only five instances of this usage, all from fiction: "we miss not having your funny face around to laugh at", "I miss not having one", "D'you miss not drinking very much?", "Did you miss not 'aving me to talk to?", and one that, interestingly enough, uses both the "miss not" and "miss" constructions in a single sentence:

"I often think I miss not having someone with whom to share the joys of Dickie, far more than I miss having someone with whom to share my worries."

The Corpus of Contemporary American English, however, has 20 instances of such usage (leaving out phrases like "miss not only…"), from news, spoken TV programmes, magazines, fiction, etc., e.g.: "BH: Do you miss not having children? Calhoun: Yes. You know I love kids", "Do you ever miss not having a daddy?", "I will miss not being able to walk Christie down the aisle", "I miss not having the late Red Auerbach to answer such vital questions", "I miss not being able to talk to people in the market", "I miss not being in a more cosmopolitan city", "'Do you miss not having hands and feet?' Well, I've never had them.", "I miss not being able to see my friends' faces", "I miss not having my dog around", "I feel that as an only child she may miss not having siblings later on, as an adult.", "I kind of miss not being able to drop by my parents' house during the week", "Cmdr. VERNOSKI: Listen, do you miss not having my long hair on the rug? Col. VERNOSKI: Absolutely! I miss not having your long hair in my hands."

It does contain one "correct" usage of "miss not" as you and I seem to understand it:

about having the disease? […] I miss not having to think about this. I miss just going to work and leading…

Of course, probably the two corpora aren't the same size, but I don't (from looking at them) see any clear justification for calling it a British construction. And from the relatively small number of instances, it seems less frequent than the "miss having…" variant.

Another way of looking at them is through Google n-gram viewer. I don't think this is extremely reliable, but worth looking.

Here are "miss having" and "miss not having" in American English:

And in British English:

Similarly, here are "miss being" and "miss not being" in American English:

And in British English:

So from the data it seems (look at the numbers on the y-axis carefully) that "miss not being" and "miss not having" are used at about the same frequency in both American and British English. But "miss having/being" are used much more in American English, so the "miss not" forms are more common in British English relative to the standard forms. Still, less frequent. (This is a crude search without context, so all the caveats apply.)

Edit [2011-11-23]: The Language Log has had around 75 posts on this very topic. It has been enlightening reading several of them, but I am too exhausted to summarise them here, and I recommend you to read those posts directly.

This definition of smurfing comes from 1996 and the game Warcraft II when certain well-known players made up new names, pretend to play badly, then beat the other players. They picked the names PapaSmurf and Smurfette.

It was used in alt.games.starcraft, and defined in April 1999 as:

someone who makes a new account then pretends they are a newbie.

An origin was offered in the same group in February 1999:

How prevalent do you think fake newbies are? You know, good players who
lure real newbies in for an easy win. Why do they get their jollies from
doing something so stupid?

I think it's interesting to note, however, that this kind of
thing was started in Warcraft II days by Shlonglor and his buddies,
who seem to be demi-gods for some people. They called it smurfing and
Shlonglor's stated reason for it was because they couldn't find anyone
who wanted to play them. So they started picking on newbies and having
great fun 'smurfing' them, that's the name they gave it. He went on to
say how there quickly developed the habit of smurf-smurfing, great fun
he said. Yeah, and who's the one suffering from all this fun the
experienced are having? The newbie, of course. If it isn't the most
inconsiderate behaviour I've ever seen..

A Warcraft II: Glossary defines:

Smurfing

A slang term coined by Warp! and Shlonglor to mean good or famous players using fake names to hide from people then attempting to beat other players. It is only a "Smurf" if those players win.

The earliest definite use of smurfing I found was in alt.games.warcraft in August 1996:

heheh, when a really good player is depressed or is looking for fun whipping the living hell out of a newbie, he adopts a fake name and then joins game and ACTS like a newbie, then he thouroughly destroys everyone in the game. this bizzare act is called smurfing, when he said "don't step on any smurfs" he meant don't get so caught up u find a smurf, and then get the living hell beat out of you :)

There was also a reference in alt.games.warcraft that some experienced players were "probably smurfs" in July 1996.

More description:

it was started by Shlonglor, who is more than a SC player (he works for Blizzard as their webmaster). He was one of the all-time War2 gurus and was extraordinarily famous due to his war2 page ... still one of the best gaming pages ever created (although it's no longer anywhere on the net ... he took it down when he began to work for Blizzard).

Anyhoo, there came a point in Shlonglor's fame where no one but a few select individuals would play him; everyone, hearing his name, would do one of the following things: cower in fear, worship like mad, or repeatedly challenge like a newbie. In the midst of this it was virtually impossible for him to get a game.

SO ... Shlonglor and his roommate at the time, Warp, came up with a stroke of genius: make up a false name that no one would recognize and go beat the * out of newbies.

For whatever reason, the names they chose were "Papa Smurf" and "Smurfette."

From hence came the term "Smurfing."

(Shaf, 1999)

A quote by Shlonglor from 2003:

-(1996) I was the originator of the term "Smurf" or "Smurfing" to signify a famous person playing games under a fake name. Before that point, everyone stuck with whatever nickname they had and never considered changing their name or playing under fake names. It began when me and Warp! played under fake names "Smurfs" and fooled all our friends. I made a page about it and it caught on big time. Pretty soon everyone played under made-up names and you had no idea who you were playing. This practice continues to happen a TON today and you still hear about Smurfing/Smurfs which all dates back to me, my site, and my Smurf page.

And an extract from an August 1996 game report ("The Smurfs vs Spiderman(Zima), Red Barron, and Void(idiot)") by Warp!:

Well, I finally played a game worth writing a story about. It was a five player game on Garden of War with medium resources. The players involved were Shlonglor (playing as PapaSmurf), Myself (playing as Smurfette), RedBaron, Void, and Spiderman (who we later discovered was the same person as Zima/Cpl_Will). Shlonglor and I were teammates as were RedBaron, Void, and Spiderman.

And then by Shlonglor, this may be the earliest description:

First let me explain the Smurf thing. Warp and I enjoy making up names and playing people at war2. We make them think we really suck and then beat them up. But the joke was on me because Zima pulled my own trick on me. He played as Spiderman making me think he sucked. Beaten at my own game! So sad. Well we have lots of fun playing as smurfs. We talk in smurf. We smurf us some ass at war 2. I guess that is totally childish, but it sure is fun.