From Wikipedia: "The "genome" of any given individual is unique; mapping the "human genome" involved sequencing a small number of individuals and then assembling these together to get a complete sequence for each chromosome. Therefore, the finished human genome is thus a mosaic, not representing any one individual."

Members of a species share most of their genetic material with each other, but there are known areas of high variability between individuals. So to build a specific individual's sequence, it seems like they take the baseline "human genome" data, and overlay the areas that are known to change.

The article acknowledges this, though perhaps obliquely:

> “As a matter of truth in advertising, the ‘finished’ sequence isn’t finished,” said Eric Lander, who led the lab at the Whitehead Institute that deciphered more of the genome for the government-funded Human Genome Project than any other. “I always say ‘finished’ is a term of art.”

The phrasing of your parent is arguably dismissive and does little to further substantive discussion. Can one meaningfully discuss "the human genome"? As you point out, each human (with the exception of identical twins) has a unique genome. I think it's reasonable and useful to be able to say "the human genome" as opposed to "the chimpanzee genome" or "the drosophila genome".

If one would rather insist on using the indefinite article, i.e., "a human genome", one can present it without resorting to a rhetorical question replete with scare quotes.

You're right, and the next frontier in genome assembly and mapping algorithms is using graph-based genomes, where differences between individuals or populations can represented as different paths through a sequence graph. (There are lots of better explanations with pretty pictures out there with a little searching)

Not only do different individuals have different genomes, each cell from the same person will have different genomes. It is more like an "average" human genome, one that no actual cell has ever contained.