Someone should write a short story about that.
The claim is biological, not sociological.
Or, more accurately, it's like having binary machine code for an unknown ISA with no information about the CPU, and no example CPU.
Also, even if we accepted that DNA fully specifies how a cell can create an identical copy of the cell that contains it, that doesn't mean that it specifies how to create a cell from scratch. The "instructions" in DNA could very well depend critically on details of the current cell. For example, the DNA could specify se thing like "take 1% of the substance secreted in organelle A and mix it with 90% water and 9% the substance secreted by organelle B". This instruction is perfectly good for specifying a copy of the current cell, and perfectly useless if you don't have the original cell for which it is meant.
This sort of thing could very well apply at the level of the whole fetus. Details of the uterus and other parts of the mother organism may well be critical parts of the "program" described by the DNA. For example, it's easy to imagine that the early fetus follows instructions like "let this much fluid pass through the umbilical chord", or "grow horizontally until you find this much pH difference between the extremeties" or whatever other instructions that are only useful in the context of an existing functioning mother organism.
And even beyond the individual, you would have a big problem recreating the species to allow for a second generation to exist at all. In particular, even if you had a whole living healthy female mammal, you would have no information at all for how to create a male of the species, so no way to create sperm cells, so no way to perpetuate the species. So the DNA of a female mammal doesn't contain information for how to make more of the species. And if all you had was a male organism, you would lack the information probably encoded in the living female that I was discussing earlier.
As a side note, this problem would not exist for birds, where the female bird does have both male and female DNA.
What we don't know is what that function is. Put differently, what is the question?