Even destroying the entire humanity would be hard, civilization could go, we have plenty of scenarios for that, but killing every human, even the odd tribe of refugees who could survive in a cave somewhere is something else. I'd say it is the maximum extent of what our technology could do. By that I mean nuking everything we could nuke, including things like volcanoes, mass produce all the greenhouse gases, the ozone depleting ones, the poisonous ones just to release them all, have our finest biologists prepare a pandemic, we may even try to bring in some asteroids.
To sterilize the Earth we would need to destroy all the extremophile bacteria, the tardigrades, the deep biosphere,... That's not happening. Note that we are very careful to sterilize Mars rovers, so that we don't contaminate Mars with Earth life. That's how hardy we consider life to be.
That's a rather fun thought experiment. If we were outright trying to destroy the earth it'd be pretty easy! We'd just have to destroy our ozone layer again and let the runaway greenhouse effect heat the planet up enough to boil off the oceans and send the water into space via atmospheric escape. Very little can survive without water and once the water is gone it's gone. Water wouldn't return to Earth unless it came on the backs of asteroids (which would be it's own problem). The extra solar radiation would help finish off what was left.
If we were going to actively bring in asteroids, the goal shouldn't be to hit the planet with them, the goal should be to use the gravity to move the planet into a less habitable zone (https://en.wikipedia.org/wiki/Moving_Earth). We could also put all our resources into developing Grey goo (https://en.wikipedia.org/wiki/Grey_goo)
Indeed earth has itself had a few close calls with total extinction https://en.wikipedia.org/wiki/Medea_hypothesis
99.5% of life may have died during the Great Oxidation Event. 96% of all marine life may have died during the Permian–Triassic extinction event
TBH it's no short of a miracle that we're still here.