To save people time, I will give a one minute summary followed by details with verifiable online pointers to facts.

Note that this is just a theory about a motive, and will be shocking to everyone.

SUMMARY OF THEORY:

• Adam Lanza was raped by a known, convicted Catholic pedophile priest named Fr John J Castaldo when Adam Lanza was 6 years old, when his family moved to Newtown, CT, in 1998
• He never stopped thinking about the traumatic moment of being raped by “Christ on earth”, which is what priests call themselves.  He spent every moment of his life trying to rationalize it.  He never developed normally.
• Then he went to that specific classroom because there were mostly 6 year old Catholic children in that room
• No one protected Adam, Adam would show the Catholics that their children couldn’t be protected

DETAILS & ONLINE PROOF OF THEORY:

• The Lanzas moved to Newtown in 1998.  See last paragraph at http://www.washingtonpost.com/local/for-lanza-family-son-adams-difficulties-dominated/2012/12/17/3c0e8eb0-4890-11e2-ad54-580638ede391_story.html
• A known, convicted, serial pedophile priest named Fr John J Castaldo resided there from 1998 until 2001
  • Fr Castaldo’s arrest for pedophilia by law enforcement in a sting operation http://www.bishop-accountability.org/news3/2001_05_25_Fitzgerald_ConnecticutPriest_John_Castaldo_4.htm
    • He got one week in jail.  Search for Castaldo in the article at http://www.newstimes.com/news/article/A-decade-of-strange-plot-twists-306249.php
  • Castaldo was accused of  attacking a boy under “extreme threat and intimidation”, had been was expelled from his seminary for “remarkable bizarre behavior” http://www.ctpost.com/news/article/Diocese-loses-lawsuit-in-priest-sex-abuse-case-823058.php
  • Article in the Harford Courant gives more details.  He was an especially frightening pedophile. http://articles.courant.com/2010-03-04/community/hc-priest-case-0304.artmar03_1_sexual-abuse-diocese-drug-abuse
  • One of many lawsuits against Castaldo http://www.wtnh.com/dpp/news/crime/ct-man-sues-church-on-alleged-abuse#.UNFfPW80V8E
  • Castaldo has been accused of the sexual abuse of at least four boys, ages 10-14.
  • Castaldo had two disturbing psychological assessments that noted he “was fearful of his own aggressive drives,” had “difficulty accepting his own sexual urges and desires as normal,” and was preoccupied with his “unresolved sexual urges.”  See NBC 30 article at http://www.bishop-accountability.org/news2005_01_06/2005_01_19_NBC30_SettlementReached.htm
  • Fr Castaldo admitted under oath that he “suffered from a sexual sickness” http://www.bishop-accountability.org/news3/2005_01_13_Tepfer_PriestAdmits_John_Castaldo_2.htm
  • More with pointers at http://www.bishopaccountability.org/assign/Castaldo_John_J.htm
  • The Lanza’s were Catholic, and went to Fr Castaldo’s church http://www.nypost.com/p/news/national/he_prayed_preyed_lTNjJcwqMzWxFztFpWNEkN
• Now the speculation:
  • Adam is a quiet 6 year old who moves to Newtown in 1998.    Fr Castaldo was a serial child rapist, and pedophile priests have as much sex as they can get away with.   Most victims never came forward (like Adam) because they knew they wouldn’t be believed.
  • Castaldo probably had many victims, most of which never came forward
  • Adam may or may not have had autism, making him easy prey.  Adam would never tell anyone, and could be manipulated easily.
  • Castaldo has sex with Adam, and the Catholic church hides and reassigns Castaldo, as they have done thousands of times in the United States
  • Psychological trauma:
    • It is tough for anyone to grasp the psychological trauma that a child experiences when they are raped by a Catholic priest.
    • <trigger alert>
    • They think they are being anally stabbed to death by “Christ on earth”, because that is what Catholic priests call themselves.   The pain is excruciating.  They think Christ is trying to kill them, and God won’t help.  They feel grunting, and groaning, and violent movement.
    • Then the pedophile priest typically tells them it is their fault, and that they will get in trouble if they tell anyone, and that no one would believe them.  They believe they are going to hell, and don’t know why.
    • They have more psychological pressure than anyone could endure, let alone an undeveloped 7 year old.
    • The pedophile priest goes to Catholic confession, is forgiven, and forgets about it.
    • Adam thinks about that moment every moment of every day.  For years, he thinks he is the only child in the world raped by Christ on earth.  He has nightmares that never stop.
    • His first goal is to make sure that no one ever knows what happened to him.  His biggest fear is that he is caught, and will be eternally bullied for being punished/raped/stabbed by “Christ on earth”.
    • Catholic child rape, and pedophile priest protection, is the ultimate psychological bullying.
    • He can’t even talk to other children.  He never develops socially.
    • As he grows older, he sees the world differently than everyone else.  He has no help or guidance.  Everyone calls him “odd”, affirming his belief that there is something wrong with him.  He knows.  He may think he was raped by Christ because he was bad, at age 6, or he was odd.  He can’t figure out what he did wrong.  The psycological games would destroy any human mind.  Especially a 6, 7, 8 year old.  And it gets worse every year.  And he can’t talk to anyone about it, so he doesn’t talk to anyone at all.  He lives life in a complete bubble.  Even Mom and the psycologists don’t have any idea.
    • He has nightmares every single night, and can’t stop them.
    • When he matures, and finds out that the Catholic church knows about his, and no one cares, and Castaldo and other priests get no penalty, he sees a world of evil.
      • Many victims of Catholic pedophile priest rape commit suicide.  In Australia, 40 suicides have been traced back to just 5 pedophile priests who abused priests between 1960 and the late 1980s, and Catholics STILL don’t care enough to do anything about it http://www.theage.com.au/victoria/churchs-suicide-victims-20120412-1wwox.html
      • Adam Lanza would know, through his internet research, that the Catholic church paid $11 million in Philadelphia to protect Msgr Lynn, who admitted to shredding evidence about 35 known pedophile priests in 1994.  Msgr Lynn shredded this information at the request of Cardinal Bevilacqua and with the knowledge of 2 bishops, Cullen & Cistone.
    • Mostly, in Adam Lanza’s bubble, he knows that the Catholic church fights to protect known child rapists and fights to humiliate the victims.  There is no good in this world that Adam sees.  In a world where Catholics say this is God’s best church, Adam sees nothing but evil.  He did something wrong when he was 6, and doesn’t know what it is.  He has always thought he was going to hell.
    • He will commit suicide, but before he does, he will take revenge against the 6 year olds, most of which were Catholic.  Catholics never protected or helped Adam at any point since he was 6, and he would show that their children couldn’t be protected.
  • I could go on for hours, but you get the idea.  An evil brain has been created, and has been cooking for 14 years.
• New (2/1/13) In 5th grade, Adam Lanza threw up while watching a sex education video.  This would make sense for a child rape victim of a Catholic priest, who is now 11 years old and just learning about sex, reliving what happened to him when he was 6 years old http://www.usatoday.com/story/news/2012/12/18/adam-lanza-sandy-hook-student/1777525/
• Like most Catholic priest rape victims, Adam never tells anyone.
  • Adam exhibited many of  the traits of children of Catholic priest child rape, which are unique, because they think they were raped by “Christ on earth”, which is what priests call themselves.  Adam:
    • Had no real friends
    • Couldn’t relate to people
    • Never told anyone what happened to him
    • Could never be touched or hugged, according to his mother in http://www.nypost.com/p/news/local/mother_devoted_her_life_to_him_then_PADqWsNSMfrx3KnO6JnlrI
      • This is very common among Catholic priest rape victims
      • Also, the barber said he never talked, and his mom did all his talking (because being touched was so traumatic).  Worse yet, the barber shop was right across the street from the Catholic church, which may be where Adam was raped  http://www.cnn.com/2012/12/18/us/connecticut-shooting-adam-lanza-barber/index.html
• Adam goes to the school with a plan:
  • Kill the psychologist that didn’t help him when he was young
  • Kill anyone who gets in his way
  • Kill the 6 year old children, most of which were Catholics.  If Catholics didn’t protect him, he would see that those 6 year olds weren’t protected, and take revenge against the parents of those 6 year olds, who didn’t care what happened to him when he was 6 years old
    • In his world (his isolationist bubble), he can now control whether 6 year old children are protected
    • The viciousness has been developed for years, and the hatred is unlimited
    • An insane mind has been created
  • He shoots himself as soon as the police showed up.  He can never be touched.
• After the massacre, the local Catholic church, St Rose, was threatened, probably by another of Castaldo’s victims who never came forward
  • http://www.foxnews.com/us/2012/12/16/worshippers-flee-newtown-church-over-bomb-threat/
  • The other victim sees that Catholic support their priests regardless of their rampant child rape, going to the church to listen to them
  • According to Yahoo news, an unidentified male called the rectory, threatening to “kill everyone.”  “My friend didn’t finish the job,” the caller said, according to the church official.  It would make sense that this is another one of Fr Castaldo’s child rape victims.
  • See http://news.yahoo.com/blogs/lookout/newtown-church-evacuated-due-unspecified-threat-during-noon-182416799.html

There’s the theory, and is a more complete explanation than anything else I’ve seen.  If they investigate with this in mind, they will find internet sites he visited about Catholics protecting pedophile priests.  Even if his computer was destroyed, his internet provider will have a log of all the sites he visited.

Lastly, why did his brain snap that day?  My guess is that it was the anniversary of the date he was raped, a date he fears every year, when the weather, daylight, and pre-Christmas celebration by everyone remind him in ways he can’t forget.

Alternatively, it could have been because his mother said she was going to put him in an institution.  However, the bigger issue for him would have been that he couldn’t handle being touched.

This is a complete motive with an explanation for everything.  Let’s see what other evidence comes up.

UPDATES, thanks to a commenter below.

• Another known (and admitted) pedophile priest named Fr Charles Stubbs, who admitted molesting a boy in 1997, was also at St Rose of Lima Parish around that time, as proven in the Reuters article pedophile priest Fr Charles Stubbs at St Rose of Lima Church when Adam Lanza was there.  However, he may have left after 1997, and Adam Lanza arrived in 1998.  The article doesn’t make it clear whether Stubbs continued to live in Newtown in 1998.
• Stubbs had been protected and moved by multiple priests including Bishop Egan, who put him in Newtown in 1997.
• I could not find proof that Fr Donovan was at St Rose of Lima during that time period
• Regardless, with AT LEAST 2 known pedophile priests in the Newtown parish at that time, there certainly was a culture of accepted pedophilia