When you think about it, it'd really suck to be failing to prove what is in fact your complete innocence and not be able to advance other defenses that could at least get you a reduced sentence (or even acquitted—correct outcome, wrong reason).
The wikipedia article lists "My dog was tied up and I don't own a dog", which is on the face of it contradictory - But there can easily be legal nuance. For example, if I'm acting as a foster home or running a kennel, I can simultaneously advance evidence that "My dog" was tied up, while also advocating for lack of liability because "It's not my dog".
On the other hand, I've seen a ton of "I didn't do x, and even if I did do X it was acceptable because Y" where Y was the worse crime... that somehow still succeeded as a defense. Thankfully not in a court of law, but public opinion is weird.
1. The jury should not base their decision on their belief whether either side is lying.
2. The defence is expected to lie, and if the prosecution cannot prove that every single one of the defence's arguments are lies, then the jury cannot convict beyond reasonable doubt.
3. The jury should assume that the prosecution is lying by default, and acquit if the prosecution does not convince them otherwise.
The defence is expressly prohibited from lying. Lawyers have a so called duty of candor [1] outlining this. Defendants testify under oath to make this clear to them. Defence attorneys must disclose to the court if their client lies to the court (and they can't convince their client to voluntarily disclose it instead) [2].
That doesn't mean people are expected to take defendants at their word during trial, juries are allowed to decide they think that someone was lying, but they aren't expected to lie.
My dad ran into something similar while on a Jury. It was for indecent exposure
Both sides agreed that the man was in the car with his pants down (defense claimed defendant was looking for a tick on his leg). The defense argued that with the window tinting on the car window, it was not possible to see into the car.
My dad's takeaway from this was that one of these must be true:
1. Someone coincidentally accused someone of having their pants down without being able to see them, and happened to be right
These two assertions ('shooting was an accident...' and 'she was within her rights...') are not inherently contradictory, though. That's what's remarkable about Kettle Logic: genuine contradictions can be employed in a proof in a convincing (and not necessarily invalid) manner. The above can be orthogonal or complementary assertions, but they are not contradictory.
That's not kettle logic, that's a mode of legal argumentation that deals with boolean "and" constructions of a law.
If some charge requires both [A] and [B] for the accused to be guilty, then this argument is that it's neither [A] nor [B], but the defendant is innocent if they can prove either half of the argument, since the condition is "[A] and [B]", not "[A] or [B]".
Whether they were within their rights would only come into play if they had the requisite mental state (intent, recklessness, etc., as for the crime charged) in the first place.
> That means that in some cases you have to argue that you killed someone intentionally to avoid being convicted
No, you don't.
It's just if you are charged with an offense that requires intent, the question of self-defense (or any other excuse) is moot if the prosecutor can't prove intent beyond a reasonable doubt in the first place.
If you are charged with an offense that doesn't require intent, like involuntary manslaughter, you don't have to argue intent to kill to use self-defense as an excuse.
And even of you are charged with an intent crime, you don't need to grant intent to argue self-defense.