The second sentence is a statement of fact in the world of genetics, phylogeny, and taxonomy. Your criticism of it tells me you are not adequately knowledgeable about these areas of science to participate in this conversation at the level required.
My point is that all three statements are true, but that in the later two cases the otherwise "socially constructed" boundaries are so useful and so meaningful to people that to say they "don't exist" is very odd.
There is no clear boundary between blue and green (and some cultures have a word for green-blue), but nobody goes about saying that "colors don't exist."
Ditto embryos. Genetics, phylogeny, and taxonomy provide definitions, which are socially constructed based on ground truth and utility for purpose. Each definition is "socially constructed" but to say the categories "don't exist" because they are socially defined is nuts.