Kratos' justification. Not entirely wrong, since many time he must kill innocent bystanders if he want to survive. The Olympians' justification is more like Moral Myopia.
Guy of Gisborne from Robin Hood is of the Virtue Is Weakness variety in regards to his pursuit of his ambition, but also a little The Way I Am in that he is well aware that he has "committed heinous crimes." Only he isn't prepared to do anything about it except to rely on Marian to "wash away his sins." She begs to differ. It does not end well.
A common justification for cliques, trolls, internet bullies and doxing (fishing for people's personal information or using it against them). Of course, the instant any of this stuff happens to THEM you can expect them to drop their "morality" like a sack of hammers.
Absolute Power: Charles Prentiss. He's a bastard because being a bastard works. You might wish it didn't, and he has some sympathy with that viewpoint. But it does.
Tywin Lannister (and pretty much every other Jerkass in the series) in A Song of Ice and Fire / Game of Thrones: Westeros is a Crapsack World where doing the honorable thing will get not only you but probably everyone around you killed. A little Pragmatic Villainy, on the other hand, can help stabilize the kingdom and make sure that most people can continue on with their lives.
As with the series theme, such actions always have a cause and effect, when you ephaized with the latter over the former. By the time Tywin dies, all the fear and hatred against the Lannisters past actions comes back to bite them, as everyone now wants to oust the Lannisters, and their hold over the realm crumbles under Cersei Lannisters reign.
Least I Could Do will twist itself into storytelling pretzels in order to let Rayne be a Jerkass wish fulfillment character and still look like a good guy in the end, usually by pulling a justification out of thin air that leads to everyone apologizing to Rayne and saying he was right all along. In one arc, Rayne's company is hiring but he doesn't tell his jobless friend Issa. When she angrily confronts him and demands to know why he didn't get her a job, he says that she needs to earn it by merit rather than getting it through favoritism — and this is after weeks of comedic backpedaling to avoid telling the truth.
The Gulag Archipelago has the line, "What can I do with the incorrigible directness of my personality! ... I am compelled to utter reprimands; it disciplines those nearby."
The Way I Am
Most characters with Freudian Excuses for their behavior fall back on this excuse. Apparently, Mommy Issues are more important than self control and common decency.
This is usually the justification for the Jerk Sue. In the author's failed attempt to excuse whatever the Jerk Sue does and cast them in a sympathetic or just "assertive," they end up writing it off as this.
Sawyer from LOST is The Way I Am, with a little bit of self-loathing and a whole lot of Heart of Gold thrown in. At least, he was in the first seasons. He would usually justify his actions with "I'm not a good person."
Gene Simmons and Ted Nugent have used this in Real Life.
"Take Me Or Leave Me," from RENT, is essentially an entire song of The Way I Am justification. Most of it is on Maureen's part, but Joanne does a lot of justifying and refusing to compromise by the number's end.
Organization XIII use this kind of excuse for their actions. Since they're Nobodies, who don't have hearts, it's simply in their nature to screw with the universe and the heroes, but it's clear from the start that 80% of the excuse is Moral Myopia.
To be fair, the whole "missing a heart" bit makes them sociopaths by design. It's rather easy to be a jerk when you're completely incapable of empathy.
Sam Puckett on iCarly very much this type. Has had another character say outright that it would be weird if she didn't make them miserable, simply because Sam refuses to grow up or act maturely.
Could very well be a Freudian Excuse, because in a later episode, it's revealed that Sam's mother, Pam, is exactly the same way.
Damon on The Vampire Diaries has used "I'm a vampire" as an excuse for his behavior a few times. It would be a lot more convincing if not for the behavior of several other vampires demonstrating that it really isn't one.
Scott Kurtz. In a webcomics weekly podcast with his friends, they actually point out this has caused him to be alienated amongst pro print cartoonists and he responds by saying that other cartoonists are jerks so he should be able to be one as well.
"Would you rather a doctor who holds your son's hand while he dies or ignores him as he gets better?"
Then again, it really is justified. House is an amazing doctor, which is pretty much the only reason he's still working at that hospital, despite being an utter jackass. The above quote exemplifies his commitment to the Good Is Not Nice trope.
Barney Stinson from How I Met Your Mother uses all three types with great abandon and inconsistency, depending on whichever one will best get him out of a conundrum without admitting he's wrong/non-awesome or showing weakness: when his friends call him out on The Way I Am by saying they're sick of "dealing" with him, he insists upon Moral Myopia. When they prove Moral Myopia wrong by showing him how much damage his jerkassery causes, he falls back on Virtue Is Weakness. When they argue against Virtue Is Weakness by demonstrating that they're all happy without being jerks, he seizes on to Moral Myopia to dismiss their opinions as signs that they're "lame" and then insists upon The Way I Am, because he's "awesome". And so it begins again.
For some people, especially if one browses internet forums long enough, hang around trolls and jerkasses long enough and you might start to become a jerk yourself and justify it by saying "everyone else is doing it, so I may well be one as well."
Also, if you start a thread asking why people are so mean on the internet, expect the users, especially the trolls, respond with "It's the internet. We can say whatever we want.".