If an asteroid was large enough to instantly kill all of the dinosaurs living all over the planet, then yes, it could certainly have the potential to decimate all multicellular life. But such a large asteroid hasn't struck Earth since the creation of Earth's moon, as per the Giant Impact Hypothesis.
You must understand how fragile life really is, and how easy it is for an ecosystem to be irreparably damaged and consequently collapse, resulting in extinction of several, if not all, species native to that ecology. A working ecosystem is a living symphony and all the various iterations of life are its notes. If you take even a few notes out of a symphony it turns into a cacophony, order turns to chaos, and life turns to death.
In an asteroid-related extinction event, the asteroid itself is merely the proverbial "finger of God" that topples the first domino. The falling of the average extinction-causing asteroid, kills barely a few tens of thousands. But then the dust and smoke rise, and covers the sun. A very large area goes into perpetual night, global temperature plummets, in a matter of weeks, plants start dying without the sun, In a matter of months herbivores start dying without the plants, and then carnivores, without herbivores. Eventually a few key species that hold the ecosystem together, die out, or most often, their numbers become too small to have impact anymore. Without the key species, the ecosystems starts to crumble and then eventually over the years, collapses entirely.
The devastation initiated by an asteroid can potentially continue for several millennia, killing billions in its wake. But thankfully so far, enough have always managed to survive to continue life on this planet. So far, 99% of the species that have ever lived, are now extinct because of various factors. And all this wonderful, incredible variety of life we see is just a meager 1% of what this planet has known.
