For example, Lebanon is an Arabic-speaking country. However, many parents insist on speaking to their children exclusively in English or French and refuse or severely limit the use of Arabic. Is there a linguistic term for such a phenomenon? Does this phenomenon occur in other countries or societies? Is it detrimental to language acquisition?
I think this is called diglossia which is a a kind of bilingualism in a society in which one of the languages has high prestige, and another of the languages has low prestige. There were and are lots of societies where that occurs, many of them are mentioned in the articles I gave the links to above. For example, in the 18th - early 19th century Russia French was a high prestige language while Russian a low prestige one, the aristocracy very often had French as L1, for Pushkin, the gratest Russian poet, French was L1.
In Britain it is very common for parents from the Indian subcontinent to talk to their children always in English rather than in Urdu, Panjabi, Gujarati etc. They believe that they are doing their children a favour. In fact, first generation British-born South Asians very often go through their entire life speaking English with an Indian accent, acquired from their well-meaning parents.
To my knowledge, there is no single term that describes this situation. It is merely one of the many configurations that arise in multilingual environments.
Also, there is not just one single way in which this arises. The examples could be.
- Parents do not speak each others first languages and communicate using a third language.
- One of the parents speaks a language of the other parent who does not speak the language of the first parent. The children are only exposed to the language of the other parent.
- Parents only speak a third language to their children to speed up their integration and/or promote their linguistic skills in another language.
All of the above can happen in all sorts of combinations of linguistic environments. For example, the neither of the parents speak the dominant language of the country they live in or one of the parents speaks the local language.
There are also various scenarios of prestige and power that will influence how this will play out.
So it seems that one term would simply not be able to describe this phenomenon accurate but it is possible that a term is used somewhere in the very specialist literature on bilingualism.
Another place to look would be research on language contact and especially creolization which often arises in contexts where children acquiring a third language is common in a linguistic area.