How would you argue such claims, geographically and/or accurately speaking? — Other than: that’s how I was taught it is; or that’s how my favourite teacher/book/source-with-some-authority says it is.
There is no generally-agreed-upondefinition for “continent”, in the same way that there was no generally-agreed-upon definition of “planet” prior to the IAU 2006 General Assembly.
Continents are identified by convention (and there are a few competing conventions) rather than any strict criteria.
I was taught (in Europe) that there are 6 continents, 1 of which close-to-uninhabited: Europe, Asia, Africa, Oceania, America, Antarctica. This convention is the same as the one for the UNSD “continental regions”. The five interlocking rings of the Olympic flag represent these five inhabited continents.
There’s another convention that considers Eurasia to be a single continent. And another that even considers Afro-Eurasia to be a single continent.
As an Australian, inculcated with the orthodoxy that this was the largest island while also being the smallest continent - how does 'Oceania' fit with your quite technical 'big contiguous mass of land'?
If we made another small rut parallel to either Suez or Panama, would we add 1 to the count of continents?