Yes, I figure those are among the most frequent arguments put forward ^^
1) Humans have completely screwed up the natural world through pollution and mass killings of plant and animal life.
Yes, the human influence on nature, especially in the last century, has been rather damaging. But I can see two reasons not to destroy ourselves because of that.
1) Mass extinctions have happened before, and nature has always survived. In fact, mass extinctions are largely responsible for the diversity we see today; nature has never been entirely stable. The biggest harm we're doing is against ourselves. Instead of destroying ourselves, shouldn't we try to correct our behaviour?
2) Pollution is mostly coming from first world countries and big countries in development. There are tons of populations and tribes, however, who live in 'harmony' with nature. Wiping them out with us would be unfair, unethical, and criminal.
2) They've also subjugated many animal populations. Animals used as resources being the most notable, as they abuse and torture them almost all the time. (These would be animals such as cows and pigs.)
Domesticating animals without torture is possible though, and some animals profited from that in history. I don't see that as reason enough to wipe us out.
3) The level of harm and destruction is not limited to life outside of humanity as there is plenty of needless war, murder, and other acts of random violence.
Again, then let's correct this instead of deleting everything. You're saying that wiping out humanity would cause peace, but it wouldn't. There would no longer be any war, suffering, peace, or joy. Because there would be no human around anymore. If you want peace, you got to fight for it (by 'fight' I don't mean violence, but perseverance).
Edit: In a way, destroying humanity is a kind of Catch-22 situation. We cannot kill off all of humanity in one instant (even if it was technically possible, which it isn't). Consider nuclear plants: if abandoned, they would end up overheating and exploding; there would be Tchernobyls and Fukushimas all over the planet. Clearly this is not an option if our primary goal is to save the planet. This means we would need to gradually opt out of any technology that pollutes the planet. Once that is done, however, we would have no reason to wipe out humanity anymore.