I can talk about Argentina. Woman/male greetings are most commonly with an “air kiss”, as mentioned above: you gently touch right cheeks while possibly doing a kiss sound. A hand shake between man and woman is not necessarily awkward, but shows a high level of formality. So, basically, as a male I would probably hand-shake with a woman in a formal/professional situation. In any situation where the introduction is as friends of friends, or situations like that, the kiss is mandatory.
Also, over the last three decades or so, male-to-male kiss has become the standard among friends. So when a friend introduces me his/her friend, it is sometimes confusing whether to shake hands or to kiss. The more informal the environment, the more common the kisses.
In Latin America you should not kiss somebody when meeting for the first time. It is very safe to do a handshake in the beginning for all kinds of situations, business, casual, etc. People will not think it is awkward but more like you are formal person. Afterwards, you can say goodbye (or greet in another time) with what other people referred as the air kiss.
During high school I remember that if you really liked a girl, there was a nice way of playing suave, where for greeting, you would actually kiss the cheek but slowly and with passion, like a 2 second thing. But of course, this is with a girl who was kind of flirting with you already.
In Southern Europe air kissing, or cheek kissing, in a professional circumstance is highly discouraged and should not be done prior a meeting or an interview. It does not matter whether the person is an acquaintance or just being introduced.
Of course, this etiquette might vary depending on job position and industry this one takes place though my first paragraph is taken as ideal when approaching a professional level.
In addition, South Europe is a vague definition and different traditions are found. In Spain it is common to give two kisses but in Italy varies from south to north, as it happens with France, even where sometimes is 3, or in Greece/Cyprus which etiquette in kissing can include two men being introduced as well.
Unfortunately, I don’t have professional experience in Latin America however, socially, the approach given can be also determined for the person to be introduced.
In this case is also quite funny seeing how the native extends his/her hand to shake it and the “new” person gets closer to give a kiss instead of the other way around.
It is more like air kissing than cheek kissing here in South America and pretty much all over Central America too. You basically put your cheek against the one you are greeting and kiss. Only one kiss and we usually go for the left side, meaning each one has their head to the left of the other with the right cheeks touching.
In social situations, even if you were just introduced, women or a man and women will cheek kiss. If you extend your hand instead, they will act surprised. When I was traveling in the area and not living here, I often mistakenly extended my hand and got a comment saying something like Oh, American-style greeting while I usually followed with a cheek kiss to show that I am trying their customs. If you don’t, they are unlikely to get ofended as they are generally understanding of people having different customs. At parties this makes for a string of people standing up to kiss when arriving and leaving, as cheek kissing is the standard gesture for goodbye too.
In business situations, both the handshake and the cheek kiss are common. The first one who starts the motion seems to decide. As I am usually uncertain and somewhat shy, I just hold on a second and see what happens. The last 3 women to interview me here all went for the cheek kiss. Although I have spend considerable amount of time all-over South and Central America, I have only been in business situations in Ecuador and Peru, so business etiquette may vary from my experience.
The quote you state from Wikipedia is accurate and interesting as I had never given much thought to self-introductions. The last time it happened to me there was indeed no cheek kissing, just a verbal pleased to meet you (mucho gusto in Spanish or muito prazer in Brazilian Portugese).
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