NOTE: This is long because I'm working out what I think about these ideas, not because I'm arguing with you about anything. So it meanders a lot and I wouldn't blame you for not reading it. Just don't read it as some kind of rant against what you said, because it's not.
SPOILERS
They don't even sound like adults talking to other adults because of this over-explanation.
Is there a moment when this type of conversation happens without DiCaprio in the room? Because otherwise it seems perfectly reasonable to me, given the preposterous circumstance. They have one day down to one moment and one chance to reveal his insanity to him, and it seems to me they'd have to use a variety of intellectual and social devices in order to achieve this. He HAS to get it. They're going to make it impossible for him to not get (aside: as an audience member, in that watch tower, I didn't mind this, and I really also think it's the most transparently humorous moment of the movie in terms of genre deconstruction and bizarre expectation reversal, and I really felt myself passing through the phases of acceptance myself [given the preposterous circumstance]). You are saying his mind was more developed than a child's, but I'd say that specific point of comprehension would be extremely difficult for him to reason.
I can't really recall any scenes where DiCaprio is not there. Your argument makes sense for the scene where they finally tell him what's going on, but what I'm talking about is a problem that runs throughout the movie. The dialogue is all very expositional. I couldn't pick up on any subtext in the film because I felt like it was all verbally spoken, down to the motivations and why everyone did what they did. I suppose that could be reasoned away with the fact the Teddy is crazy and half the people he speaks to don't even exist, but I found it difficult to reconcile that with me as an audience member having to sit there and have these things effectively be explained to me as well as to Teddy.
It's like how some people here found it funny (you say you find it humorous as well) when Ben Kingsley reveals that board with the anagrams on it. I felt like that was what the dialogue was doing all the time. If the whole style of the dialogue is about how you explain things to a person with limited reasoning abilities, then the movie still doesn't give the audience any additional work to do, effectively making it so that everything that happens is explained verbally to us in simple terms. I felt like I never got the chance to discover anything that wasn't explained verbally to me.
Now that I'm thinking more about it, I think one of the problems that I have with it is that an insane person's mind is not simply like the mind of a child--an essentially normal mind. An insane mind has an inability to reason properly, so the notion of talking to Teddy in a way to make it impossible for him not to get doesn't really work. They're explaining it to him like he is a sane but stupid person, a poor tactic for Teddy, but a great tactic for the audience (except, not really).
Also, the notion of a person "going insane," such that they were sane and, due to a single traumatic event, become insane, seems dubious to me.
What I'm suggesting is a story where the Leo character really did just land on that island a few days ago and by the end of this experiment, was made to believe that he had been there for years.
Obviously a direct and unintentional contradiction here. For a number of reasons. How many days does the film take place over? Four, maybe five? You're saying it's more likely for man to be convinced, in five days, that he's been on an island for years and didn't realize it (!), even though he probably came to the island sane, and has little emotional investment in any of the people there, then for a man to go nuts because his fucking wife murdered the goddamn kids in a super weird and thoughtless way! Get out of town. Does the film specify that Leo went immediately nuts, that a helicopter was flown in to lift him out of the backyard because he was so immediately insane? To me, the guy could have gone nuts, however long it took, and he definitely didn't have to be insane to kill his wife in that moment.
Well, I'm really talking about two different things here, so I should clarify. The first clarification is that I was definitely talking about a different story, not this story. I didn't mean it as a suggestion to change this story, but rather that it made me think of another kind of story that I would have found more intriguing.
I don't really know much about mental insanity from a psychiatric point of view, so I was just saying that I am under the impression that, for actually mentally insane people, there are chemical and/or physical defects in the brain that were always there, and not caused by a single traumatic event. While a traumatic event could trigger apparently insane behavior, the lack of sanity was always there, such that a sane mind cannot become insane, barring physical damage to the brain. The length of time (whether Teddy went instantly crazy or went crazy over a longer period of time) doesn't matter. Oh, and I neither suggested nor thought that Teddy was insane when he killed his wife; that action was reasonable given the circumstances (i.e., sane).
So anyway, the other story that I was suggesting would be based on an experiment whereby a sane person is isolated from society, expose him to strange things that are performed by actors which he cannot fully explain, and then later explain to him that his actual life was imagined and that he has physically been in this place all along. The reason that this would be intriguing to me is because you can always logically explain that the things that you thought were real are not real (in the way that Descartes logically proves that he cannot know that the world exists at all outside of his mind). There does actually exist a logically sound explanation as to how everything you think is real could actually be imagined. A sane person would be able to logically follow the explanation, and the experiment would be to see whether that, in the context of inexplicable happenings (which are actually performed by actors) could, over time, convince the sane person that he has been insane all along--not that he once was sane and became insane, but that he was always insane. It would be explained with such strong logic that it would be sane to think that you might be insane. Interestingly, you would have to be sane in order to be convinced of this, because one of the hallmarks (as far as I've heard) of actual insanity is an inability to fully follow logic. So, if you can be convinced that you are insane, you are probably sane, yet it still remains possible to be convinced that everything you thought was real was actually a dream or trickery.
This is a seriously considered thought in philosophy (though normally discussed in terms of the existence of the world, rather than whether you are sane or not), so this story idea would be to take the thought experiment into the realm of an actual experiment. Maybe a better way to put it is not to convince a sane person that he is insane, but rather that everything he ever thought was real was in fact not real, and that he has physically been on this isolated island for years while imagining a life elsewhere. This is a very different story than the one in Shutter Island, but I brought it up because the movie made me think about it.
But I just wanted to clarify that I don't think it's a contradiction because the story idea would not require that a sane person actually becomes insane, but rather is made to believe that he has always been insane, and that if he were to realize that his ability to follow that logic means that he's not insane, he may still be convinced that his real life was actually invented in his mind (which is not the same as insanity).
Which now actually makes me think that the Teddy character in Shutter Island is not technically insane, but is instead suffering from something closer to what Leonard suffered from in Memento. He must be sane if he can be convinced, even through super obvious explanation, that he is insane, at least if we're subscribing to the notion that insanity specifically involves an inability to follow logic. That makes Ben Kingsley's notion that he can simply talk a person out of their insanity or let them play out their insane behavior until it has passed ridiculous.
But again, to clarify, I don't really know anything about real mental insanity.
