The scene is partly about the rigid rules of formality interfering with enjoyment of the food as others have hit upon.
The real joke of the scene though that makes it so funny is that the teacher is teaching the girls not to slurp their noodles. It's the girls' natural habit to slurp the noodles, as this would be proper japanese etiquette.
The teacher is teaching western etiquette, so that if the girls go to, say, America, they don't embarass themselves by slurping where it would be considered rude. She's teaching gaijin (foreigner) etiquette to the students for when they travel.
They hear the slurping and look over to see that the person making the noise is not Japanese, but a foreigner who has learned the Japanese way of eating noodles, perhaps because someone taught him etiquette back home. They're spending so much time learning not to slurp while the gaijin is over there slurping away happily. Seeing a foreigner do this, they figure it must be okay and it all makes the western etiquette teacher look silly.
Edit: hah. I went back and realized that it was Italian spaghetti they were eating, in which case it would be improper to slurp. So the foreigner has emulated Japanese noodle etiquette but applied it improperly to spaghetti, and the students trying to learn about what westerners do emulate the only westerner in the restaurant. So first he imitates the Japanese and they imitate him right back, and nobody has it right, but all are enjoying.

It must be boring to be simpleminded like you are, agentbach.

Why is it so hard to beep understand it for some of you people. The teacher's teaching how to eat the spaghetti the western way, the girls see a western guy slurping down the the noodles and therefore they assume he must be eating it the right way because he's a western man and since he's from the west, he must know how to eat it properly. Stop over thinking the beep and trying to pretend to act intellectual and cultured.

Every time I see this scene it reminds me of what Sophia Loren said: Spaghetti can be eaten most successfully if you inhale it like a vacuum cleaner.
Rome. By all means, Rome.

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Actually I think it's a way of celebrating slurping. The scene suggests that rigidity and propriety restricts enjoyment of food (anyone who's slurped noodles can attest to that) and the women attending the etiquette class didn't seem to enjoy themselves, as opposed to the Westerner clearly having the time of his life allowing his tongue to taste every centimetre of pasta passing through his mouth. In the wider scheme of things, the pursuit of happiness is similiar to the pursuit of taste, which in this case means we shouldn't be too hung up over rules/formalities.
If I remember correctly, the instructor herself finally relents and joins the slurping contingent. Her surrender drives home the point about pursuing taste/life/happiness/allthingsunshine with abandon. I loved it.

pwillener is correct. it is also important to point out that many Japanese chefs/owners would be offended if their noodles and soups weren't slurped loudly.
this is changing in the East, but slowly and slightly.
take pleasure in how far you've come

The teacher earns her keep by teaching etiquette. She may make things up to underscore her authority, or teach out-dated rules for politeness. The loud foreigner exposes her as a fraud, and the students mutiny and decide "to hell with her."
Even she gives in and slurps loudly. It's a hoot.

The scene is obviously played for comedy, but on many levels of perception. The comedy of the teacher teaching asians how to eat noodles (compare to the Master in the film's opening sequence) is juxtaposed with the comedy of the students slavishly following the example of the foreigner. There is a comedic double-entendre in the Japanese hostess counselling her class to eat soundlessly, while the exemplar foreigner (who is a lout) makes a horrific amount of noise; both extremes are presented comically, and the hostess eventually relents and eats as loudly as anyone, out of the presumably Japanese desire to conform. Conformity is treated comically in an adjoining sequence, with the Corporate Bosses all ordering Sole Meuniere.

The point is that Japanese slurp every kind of noodle very loudly. The teacher was trying bring Western etiquette to the girls, but when they heard/saw the American slurping, they all fell back into their true natural habits (including the teacher!)

My interpretation is that they (the students) were being very rigid and formal rather then just enjoying the food for its own sake and when they saw the american doing that it just sort of caught on its just a way of reflecting the over all feel of the film

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You waste the only life you believe you get by sitting in front of a computer verbally sparring with other time wasters. You Time Waster. Seems like the amount of time and effort you spent in front of the computer trying to annoy "fundies" you could be using to do something constructive before you "rot in the ground". Just a suggestion. By the way don't bother responding, I won't be reading.

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I guess the thing that triggered my question about this was about the Japanese culture. The students seem to totally disregard the teacher of etiquette in this scene. I don't understand if it is so acceptable for them to suddenly ignore their teacher and chose to follow the habit of a stranger.

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Obviously because he is a foreigner and the students think that he knows the proper way to eat spaghetti. Spaghetti is a food to be enjoyed (and I do) but I never, ever slurp.