I was always taught it was 7. Europe, Africa, Asia, NA, SA, Antarctica, Oceania.
The contention is usually around Oceania, because there is only a single large landmass (Australia), and none of the other countries are attached. There's precedent for that, obviously (UK/Iceland is Europe, Carribean is NA, Japan is Asia), but in all other continents (besides Antarctica), the majority of its nations are part of the main landmass.
Just having Australia leaves several countries without a clear continent. Is NZ part of Australia or Antarctica? Is Malaysia part of Australia or Asia.
The fact that Australia is also the name of a country doesn't make it appealing for others to recognise as a continent they belong to. It's too easy for the two names to be misused, and to suggest a deeper geographical/cultural/historical connection between the other nations and Australia.
And this is why identifying continents is tricky. It is not just geography.
The reason the divide between Europe and Asia is so fickle and arbitrary is because it is based on culture and heritage, as well as a 2000+ year old tradition. Typically Europe consists of the nations of combined heritage, who have a shared history, and therefore stops at Turkey (although Turkey gets closer to being culturally European in recent centuries).
The divide is justified in that the countries in Europe have more in common with eacnhother than those in Asia. But what of the countries in Asia that have equally little in common with other Asian countries? Afghanistan shares no heritage with Korea. India shares little in common with Japan.
If we divide Europe and Asia up by culture should Asia not be split in three? West Asia (Middle East, Asia Minor), Central Asia (India, Pakistan, Nepal, Bangladesh) and East Asia (China, Mongolia, Korea, Japan).
Each continent is defined by different things.
Europe is cultural.
Asia is a product of not having Europe's culture.
Africa is geographical/cultural
NA/SA are geographical, although the divide between them and Central America is cultural too.
Australia/Oceania are both geographical on two different measurements, but are contested on grounds of culture.
Then if you want to throw in plate tectonics as a qualifier, it gets even more confusing with some continents clearly defined and others who are split up more.
I say there are 7, but what those are is not always clear.
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