The general level of fear about human extinction (in the near term) is very low. It is not an outcome considered by many as a credible risk (excluding religious extinction). .
Suggested reasons for human extinction's low public visibility:
There have been countless prophesies of extinction throughout history; in most cases the predicted date of doom has passed without much notice, making future warnings less frightening.
However, a survivor bias would undercut the credibility of accurate extinction warnings. John von Neumann was probably wrong in having “a certainty” that nuclear war would occur; but our survival is not proof that the chance of a fatal nuclear exchange was below 90%.
To prevent public panics, official reports containing high casualty estimates are sometimes suppressed or changed (such as Admiral Rickover's critical report on nuclear industry safety).
Extinction scenarios (see below) are speculative, and hard to quantify. A frequentist approach to probability cannot be used to assess the danger of an event that has never been (and never will be) observed by humans.
Nick Bostrom suggests that extinction-analysis may be an overlooked field simply because it is too depressing a subject area to attract researchers.
Some anthropologists believe that risk perception is biased by social structure; in the "Cultural Theory of risk" typography "Individualist" societies predispose members to the belief that nature operates as a self-correcting system, which will return to its stable state after a disturbance. People in such cultures feel comfortable with a "trial-and-error" approach to risk, even to unsuitably rare dangers (such as extinction events).
High technology societies tend to become "Hierarchist" or "Fatalist" in their attitudes to the ever-multiplying risks threatening them. In either case, the average member of society adopts a passive attitude to risk minimization, culturally, and psychologically. T
The threat of nuclear annihilation actually was a daily concern in the lives of many people in the 1960s and 1970s. Since then the principal fear has been of localized terrorist attack, rather than a global war of extinction; contemplating human extinction may be out of fashion.
Some people have philosophical reasons for doubting the possibility of human extinction, for instance the Final anthropic principle, plenitude principle or Intrinsic finality.
Tversky and Kahneman have produced evidence that humans suffer cognitive biases which would tend to minimize the perception of this unprecented event:
Denial is a negative "availability heuristic" shown to occur when an outcome is so upsetting that the very act of thinking about it leads to an increased refusal to believe it might occur. In this case, imagining human extinction probably makes it seem less likely.
In cultures where human extinction is not expected the proposition must overcome the "Disconfirmation bias" against heterodox theories.
Another reliable psychological effect relevant here is the "Positive outcome bias".