What is the meaning of Teddy's last dialogue in Shutter Island?

To Live as a Monster

If he accepts his guilt and becomes sane he will become the Monster. His delusions are his brains way of removing this guilt and hiding the fact that he ignored his family, did not act on his wife's mental illness, allowed her to murder their children and then murdered her. By accepting what the doctors are telling him he will need to go on living in the knowledge that he allowed terrible things to happen and did terrible things. The doctors will be able to treat him without a lobotomy but he will be fully aware of the crimes he committed.

To die as a good man

In his delusion he is a good man. He truly believes that he is on the side of law and order and that he is doing right. If he chooses to continue to believe this he will be lobotomised and will no longer have relevant brain function to question what he did or did not do. The death is not literal as the other answer suggests. It is about the fact that if he continues to believe he is this good man he will be lobotomised and effectively "die" believing in this. He will not die in a literal sense until later, but he will do so in the belief he was a good man.

What is most exciting and cathartic about this decision is that this appears to be a moment of lucidity where he understands what has happened and is not in thrall of his delusions. He at this point of lucidity makes the decision that he can not live with his crimes and would prefer to lie to his doctor as he knows this will result in his lobotomy.

By making the statement to his doctor he makes him aware of this also and by virtue of this you could also argue that he is being a good man by electing to be punished as well as the belief in his delusion that he is good.

Both cases are Teddy, himself, and he lives this duality.

In one case, if he acknowledges he is the killer of his wife (and indirectly his children because he was away so long and often he never noticed his wife's depression), he is the 'Monster', but he can continue to live here on the island in peace, since he will accept the lobotomy. If he refuses to acknowledge his guilt, assuming the mantle of 'Good Man', and pursues trying to get off the island, he will certainly die during the attempt, since the island is remote, and the guards heavily fortified and 'itchy' to shoot someone (Remember that a prison is as much a prison to the guards, who spend long days languishing for something to do).

Teddy is sitting on the staircase when Chuck arrived and then sat beside him. Get his cigarette offered him then both start smoke. Chuck starts a conversation with him by asking "so boss what now?" Chuck was about to test his patient by pretending again to be his partner. This is I think a usual way to monitor a patient with mental illness.

I think Teddy already knew that chuck was only testing him and he just plays along with Chuck, answering and acting again, like the character he created in his fantasy, deceiving Chuck. So Chuck nods to his colleagues showing negative gesture to them.

Then Teddy asks a question which surprised Chuck and makes him wonder. Teddy's last dialogue "Which would be worse? To live as a monster or to die as a good man?" Teddy deceived chuck by pretending he is still living in his fantasy world resulting a go signal to the doctor to proceed their lobotomy operation unto him which is I think what he expected and decided to go through.

That is why he says the last dialogue. If he shows that he's okay they wouldn't perform the lobotomy on him. He will live his life full intact with his memories of the past bad and beautiful. But the consequences living with this are so hard it made him think that he was about to live the rest of his life as a monster. And going through with the lobotomy operation was about partially, in most cases almost all of your memories are wiped out of your brain and left you incapacitated for life. So in this kind of brain and body surely he cannot commit any kind of sin until he dies. He will surely die as a good man.

He has been sane the entire time. He is accompanied by a new partner (which is suspect) and has migraines due to his PTSD from his experience in world war two. He is given psych meds from the institution which is a US experimental psych ward carried over from Nazi scientists. At the end he accepts his lobotomy because he would rather live than to die a sane man. This lobotomy also is his answer to forgetting his past which is his plague (the war and his lover whom he is no longer is with). He knows that he will never escape the island and would be murdered If he were to try. The government experiment would be compromised and he realizes his only option to true serenity.

Which would be worse: To live as a monster, or to die as a good man?

Firstly it proves he is currently well and willing to be lobotomised, probably as a punishment for his crime. For this reason 'dying as a good man' does not mean he is being lobotomised when he is delusional, as he is fully aware of his crime and he would be lobotomised (die) as a monster. I prefer to view the statement 'die as a good man' to mean 'to live a lie'. When psychotic he is not living his true life, he is figuratively dead.

Therefore 'to live as a monster' means, when he is mentally well (alive and aware), he understands what he has done.

Another way of phrasing the quote would be "Which would be worse, to know I am a monster or to wrongly believe I am a good man"

You can interpret the movie a million different ways.

My interpretation is based off of the small behaviors many characters have throughout the movie. Like the guards; who in the begging of every scene involved, watch Teddy with fear until Teddy faces their direction, then they look away. The guards, the policemen and his “partner” does this constantly, in situations that do not make sense. The argument can be made that Teddy is a crazy patient and they were fearful of his violence..yet other events don’t add up with that perception.

For example, in one scene Teddy climbs down the cliff to get to the lighthouse. There was a cigarette he picked up, and a body at the shoreline which really wasn't there. The lighthouse was supposedly where Nazis did surgeries on the human brain, manipulating their thoughts and emotions..weird how in this scene, when Teddy reaches the bottom of the cliff rats come out- from what looks like man made tunnels in the rocks. The rats conveniently surround the only way to the lighthouse. This redirects Teddy to the cave with the doctor/escaped inmate.

The feeling I got from this scene was that Teddy is like a rat in a maze, constantly being redirected. I think that Teddy is perfectly sane. And that he was being redirected to the cave because someone didn't want him to see a truth they could not cover without killing him.

My explanation for Teddy’s hallucinations is this:
Nazi’s found a way to dig inside his brain before Teddy made it to Shutter Island. Somehow made it so they can make him see whatever they wanted him to see at any time, regardless of where it is. It could be physical technology, occult channeling, hypnotism who knows. If Teddy was totally nuts in the movie, that would mean he spent two years in Shutter Island.

But then how would he obtain a marshal badge or arrive on a ferry? Why would a crazy lady see Teddy and put her finger to her lips, as if to stay silent? Why would another woman write for Teddy to run while his “partner” was getting a glass of water? Why would a police officer casually speak of mind experimentation, mysticism and occultism for no reason at all? Why would a German doctor speak of pushing a good man to commit violence if he wants ideal social sanity? Why?

Because, if you really are aware, you must swear not to speak of these things. You take a vow of silence, or a vow of exposing deceit and I like my choices. It’s better to die a good man. Your crazy to think Teddy is crazy.

When the psychiatrist approve that Teddy is well and back to sanity he will be killed by the black guy carrying an ice pick hidden in the towel.

And if the psychiatrist doesn't confirm his sanity the test will continue until they believe that Teddy is not insane anymore.

To the fact that Teddy is already well, He said Which would be worse? To live as a monster, or to die as a good man? He means him as a goodman and him as a monster by killing him after the experiment.

Wow, some people are really still hanging on to the belief that all of his delusions about Shutter Island are real, and they really are Nazi scientists experimenting with mind control. The film makes it indisputably clear that Teddy is crazy and a patient at the island. The scene at the end can be interpreted as either him knowingly choosing to be lobotomized, or him relapsing into his fantasy. I prefer the former. The way Leo acts that scene, I think he was lucid and said those last words to Dr. Sheehan to clue him in that it was his choice and he's at peace with it.

The comment about monster/good man, which we know Dr. Sheehan immediately "got" was made after the Dr. Sheehan shook his head to indicate "relapse". So the question is what was the purpose of saying that? In my opinion, he wanted Dr S to know that the experiment worked - which would have been a breakthrough in terms of "treatment" options (i.e. lobotomy) at the time. However, it just wasn't for him. Daniels wasn't a "good man" - if he was he would be out trying to save ALL the patients on Shutter Island - Daniels was doing a job and there is nothing to say that he thought of himself as a "good man". We know Laeddis wasn't. Therefore the "good man" comment must be to let Dr. Sheehan know that the experiment was not in waste and that their efforts worked and by saying so, he died a good man. I.e. Your experiment worked so continue to develop behavior-types treatments instead of surgically removing a part of the patient's brain.