One might argue that it's a bad thing at the DNA level for your DNA, not for you as a person. If you make the distinction between you as a person and your genetic makeup, then there is nothing bad, since whose genes live on Earth in a thousand years is irrelevant, it could be elephants and you would be as happy.
If you go down to the DNA level, one might say that it's a bad thing, because DNA's objective is to survive and spread. Just like life itself. If the genetic makeup that makes you European disappears or is less prevalent than it was, then you could say that the DNA you carry did not reach its objective or was less successful in doing so than other groups. Even if the difference between your DNA and that of the group that succeeds is just 0.5%, your European DNA branch split from the other tens of thousands of years ago.
You could say now that whatever mutations were acquired during those years failed. Those tens of thousands of years wasted, your most recent ancestors that went through: famines, wars, disease, ice ages, etc.. might just as well have committed suicide and saved themselves the trouble (assuming you're nothing but a thing that carries DNA).
Sex is there to help the offspring of two organisms survive. If they replace themselves with 2 children, then that's 50% and 50%, even and fair. What the projection says though is that the DNA of Europeans won't be 50% European in Europe and 50% in immigrant's original countries. It would be much less than that in Europe with current trends and nowhere near in the immigrant's original countries. So you wouldn't be getting that fair share.
When did DNA get a will of its own? =)
Second, I don't think a change in the genetic makeup (which is what the projections point to) would necessarily mean the death of the Western civilization. In fact, the many Western values have already spread beyond the West, leading to miscegenation of cultures. The same would be true for an Europe with a higher number of people with different genetic makeup.
Personally, I'm more worried about the loss of local values in the face of the giant which is the US, which has much more power to disseminate them than any Muslim country.
A change in the genetic makeup of Egypt, Lebanon, and Syria from Christian ethnicities to Arab certainly lead to the death of those cultures. You don't understand that races and cultures are two very intertwined things.
. The current trends lead to a projection of a different genetic makeup than the current
. The projection is a bad thing
Therefore, the current trends are bad.
But the argument fails to address why the projection is bad. That premise needs to be justified for the argument to be valid.