The idea that it's a social thing rather than a biological thing feels like a weaker claim. At the risk of sounding a bit reactionary, it seems a bit like claims relating to sex or race: there's a lot of pressure not to discover "natural" rather than socially-constructed differences.
I love how the discovery that humans are not all the same species has been completely glossed over. Humans are at least three separate genetic lineages (maybe more) comprising of Africans, African and Neanderthal hybrids (all non-Africans), and a third hybrid made up of African/Neanderthals/Denosovians (Melanesians).
For what definition of "species" is this true? (The definition I know is, a male A and a female B belong to the same species if B can give birth to A's children who can then themselves reproduce. By this definition, all humans are the same species. This is not to say that there aren't significant genetic differences between groups of humans coming from different lineages, just that it doesn't make them different species according to the definition I know.)
The definition of a species is not limited to being able to produce offspring or even fertile offspring. Lions and tigers can have offspring (ligers) who are sometimes fertile yet I doubt anyone would consider them the same species.
More fundamentally even if we decide that all homo lineages are the one species, it is the ignoring of all these lineages and the interbreeding between them that is the interesting observation. We now know that Neanderthals did not become extinct yet this is total ignored.