An asteroid may kill a lot of people, but it will not cause global extinction. No asteroid strike has ever completely wiped out life on earth.
Just because it has never happened in the past doesn't mean it can't happen in the future. Granted, it would take a very large asteroid and it is highly unlikely, but it is possible.
By the time you get up to a mile-wide asteroid, you are working in the 1 million megaton range. This asteroid has the energy that's 10 million times greater than the bomb that fell on Hiroshima. It's able to flatten everything for 100 to 200 miles out from ground zero. In other words, if a mile-wide asteroid were to directly hit New York City, the force of the impact probably would completely flatten every single thing from Washington D.C. to Boston, and would cause extensive damage perhaps 1,000 miles out -- that's as far away as Chicago. The amount of dust and debris thrown up into the atmosphere would block out the sun and cause most living things on the planet to perish. If an asteroid that big were to land in the ocean, it would cause massive tidal waves hundreds of feet high that would completely scrub the coastlines in the vicinity.
In other words, if an asteroid strikes Earth, it will be a really, really bad day no matter how big it is. If the asteroid is a mile in diameter, it's likely to wipe out life on the planet. Let's hope that doesn't happen anytime soon!
It might not wipe out ALL life as some sea creatures might survive and some microbes would likely hang on, but a mile wide asteroid (especially a dense one) impacting at the right speed would wipe out nearly all life on Earth.
As far as detection goes, I agree that we should be looking out for them, but suppose we found one. Suppose tomorrow it was announced that scientists just spotted a one mile wide asteroid that will collide with the Earth in two months. (Let's put the impact zone at New York City just to add to the fun.) Could we do anything about it in that time? Of course, there would be panic as the entire northeast United States (and some of Canada) tried to relocate. Politicians would give long speeches (and perhaps some of the more anti-science politicians would try to block spending any money on the problem until "more data was gathered"). Even if the world rallied around the cause instantly and everyone didn't panic (HUGE ifs), do we have the technology to alter the course of a mile wide asteroid in 2 months?