Javert reveals his reasons in the song he sings when he commits suicide.
And must I now begin to doubt, who never doubted all these years/
My heart is stone and still it trembles/
The world I have known is lost in shadows/
Is he from Heaven or from Hell?/ And
does he know, that granting me my life today, this man has killed me even so...
I am reaching
but I fall and the stars are black and
cold/
As I stare it to the void/ to a world that cannot hold
I'll escape now from that world, from the world of Jean Valjean/
There is nowhere
I can turn/
There is no way to go on.
Javert kills himself because the mercy shown to him by Jean Valjean
so disrupts his black and white world view that he cannot bear to live in a world he no longer understands.
One of the key themes in the work is that those who cannot adapt are destroyed (Javert, Fantine, Enjolras), while those who are flexible thrive (Thénardier).
It is really a very cynical work when you get down to it.
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Javert was a man of big integrity and he believed fully in the law and the penalty system.
He followed and enforced the law to the letter.
So when he realized that Val Jean was doing more good as a free man that he would have done in jail he find himself with a dilemma.
He can't let him free because he would betray his integrity, but also he can't stop him because he would prevent him from protecting good people.
So he found the only solution to his inner fight.
If he dies Val Jean is free to go and he would not have to betray the law.
From wikipedia : When Valjean saves his life, Javert finds himself unable to reconcile his life's work pursuing criminals with the nobility and justice shown him by the man he thought was a criminal, and takes his own life by jumping off a bridge into the river Seine.
movies.stackexchange.com/users/5612/Maurizio In denmark
The OP has identified some of the reasons for Javert's suicide.
He does sing "
Damned if I'll live in the debt of a thief!"
but the central reason is the conflict created in his mind by Valjean's actions.
He shows this when he sings "And must I now begin to doubt, who never doubted all these years.
"
I myself have found this difficult to reconcile from a modern western perspective.
One must realize, though, that Javert has spent his life fighting the internal shame of his low birth ("I was born inside a jail...
I am from the gutter too.") with a strict adherence to the law.
In differentiating himself from the "scum" he grew up seeing he has created an inflexible dichotomy between righteous and evil men and left himself unable to see that a person can cross that divide ("Men like you can never change").
He was unable to see the good and bad in every man and did not believe a person could make such a fundamental change.
And really, men dealing with change is what the entire story is about.
The revolutionary change of 19th century France; Marius' struggle with his changing ideals; Valjean's change from criminal to upright citizen.
Each character was dealing with the internal struggle created by these changes.
Javert could not come to terms with it and the contradictions it presents.
All of this is shown in the lyrics but you have to really pay attention to the details of what Javert is saying.
Some of these details are exposed during the confrontation duet where both characters are singing simultaneously and can be tough to pick out.
I must commend the writers of the musical for managing to bring out so many of Victor Hugo's complex characters.
To take a 1200+ page book and turn it into a 2 1/2 hour play is a real accomplishment.
movies.stackexchange.com/users/19836/Tom
Victor Hugo's piece is a very interesting piece theologically, especially looking a Javert's death.
Javert represents the Old Testament, the Torah.
He lives the law, and he is the law.
Jean Valjean represents the new law, the New Testament, the law of love and mercy.
Just as in the Bible, both laws cannot coexist; one has to be done away with, one has to die.
As Jesus died on the cross, he took with him the Old Law, giving us the new law of love and mercy.
As Valjean forgives and shows grace and mercy to Javert, he lays the new law of love and mercy, thus the old law (Javert) has to die.
movies.stackexchange.com/users/33856/Shannon Riech Williams
There's a passage in the book.
Javert encounters a dilemma: if Javert were to take Valjean into custody, he would betray the humane law since Valjean saved Javert in the exact same circumstance before; if Javert were to let Valjean go, Javert would shirk his duty as a police inspector that he has always staunchly believed in.
Javert finds an inconsistency in the logic about the rule of law and his role as a police inspector.
Javert lets Valjean go, but he cannot reconcile the inconsistency between what he just did according to the humane law and his role and belief as a police inspector that carries out the social law.
This inconsistency drives him to suicide.
I believe the story takes place during Napoleon III, another rebellion against his reign that fails.
movies.stackexchange.com/users/53777/Austin Mun
In the film  Les Misérables , Javert kills himself after letting Valjean pass. Why did he commit suicide?   Was it because he felt he had failed?  Was it because he didn't want to be indebted to a criminal?  Was it because he realised he'd been pursuing a good man?   I can see these reasons upsetting him but not enough to take his own life!
What was the reason for Javert's decision?
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<plot-explanation><character><les-miserables>
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Javert was a man of great integrity, who obeyed and enforced the law. So, when he realised that  Val Jean was helping people and arresting him would prevent him from doing that he found himself in a dilemma. One that could only be solsved, without breaking the law but also doing the right thing, by killing himself. Javert was a man of big integrity and he believed fully in the law and the penalty system. 
Javert was a man of big integrity and he believed fully in the law and the penalty system. When he realized that Val Jean was doing more good as a free man that he would have done in jail he find himself with a dilemma. So he found the only solution to his inner fight. If he dies Val Jean is free to go and he would not have to betray the law. He takes his own life by  jumping off a bridge into the river Seine.