Well, yes, we could probably kill most cute/cuddly/intelligent large sized mammals, and are actually on our way to doing so, very sadly.

But... try as hard as we may, I do not think we could eradicate "all" life on Earth (not with our present technology here on the surface of Earth).

Consider: there is life at the bottom of oceans... not to mention life even 7 miles underground, currently living in SOLID ROCK, that can survive a lot of insanely harsh surface conditions.

And even if we manage to kill that deep-life somehow (shielded by 7 miles of solid rock!) consider that bacteria has recently evolved/learnt to survive on nuclear fuel rods at power plants.

So really... I don't think we could ever fully sterilize the surface of planet Earth, if we really wanted to make a conscious effort to do so.

And besides, aside from a nuclear-war, actively trying to sterilize the surface of an entire planet of "all life" would involve a lot of WORK, energy, and ongoing effort.

But as this dark-project is underway, at some point humans will die out (long before a lot of other life, such as bacteria and fungi fully die out.

So at the moment the humans die out, the dark-project would probably break down and come to a grinding hault... stopping the destructive process at that point.

That is essentially what is happening now, as humans alter the surface/atmosphere.

FURTHER...

Keep in mind that Mars is a VERY DIFFERENT planet from Earth, in an extremely different situation, that doesn't fully compare to Earth.

Because Mars' overall mass is so TINY compared to Earth, most of it's plate tectonics shut down long ago, effectively haulting mineral recycling.

Likewise, because Mars is so small, it could not maintain a magnetic field to shield the planet from constant high-energy and radioactive particle bombardment... not too mention how much COLDER and further away from the sun Mars is... etc...

And yet, even though Mars has so MANY MORE problems than Earth currently faces, in terms of sustaining life, there MIGHT be life clinging to an existence below the surface of Mars... maybe!

IF that proves to be true, then in fact Mars will become an example of just how hard it is to kill "all" life on a planet!

But anyways... "Mars life" aside... we have enough evidence here on Earth, to show just how strong life is.

HOWEVER... as technology advances exponentially this century, then there may come a point in which you are correct, and humans MIGHT be able to sterilize every last living cell on a planet...

For example, if NASA perfects technology of moving asteroid bodies... then changing the trajectory of a few large asteroids, or even moons, could completely shatter Earth to the core.

But heck even then... some bacteria encased in rock will survive, and continue consuming nutrients in the rock, even as it drifts in space...

And maybe the planet would re-coalesce and that bacteria would then recolonize the newly formed planetary body! (Or drift away to recolonize another world, such as Jupiter's moon Europa.)

So again, it can be tough to kill "all" life on a planet, once that life gets a foothold.