Sorry for the delay. I was busy and your question is very complicated and needed a proper response. I will write in English so that others might find the response useful too.
We have to know the history and socio-political factors that make cold hearted mass murderer out of people. We can not form simplistic and moronic views on such phenomenon without knowing the depth of the issue. For instance, how Hitler becomes Hitler and mass murders tens of millions of people? How Stalin a mediocre and frail person manages to drive back Lenin and take over Soviet Union, causing one of the biggest mass murders of human history? We can not go on and answer these questions without knowing the history.
The group that has caused this latest mass murder is actually a follower of Deobandism. Almost all the horrible things that are happening in South Asia and attributed to "Muslims" are actually the doings of Deobandis. As you might also know Taleban were also Deobandis. So are the scumbags in Iranian Baluchistan. Now Deobandism has a very peculiar history shrouded in lots of secrecy. We don't exactly know what motivated its founding fathers to make it and for what purpose, but we know that they did. And boy, they were successful. But I can give you a condensed version of their history so that you can go and understand these people and the phenomena they cause better.
It all starts with Indian rebellion of 1857. What the Indians themselves call "Jang e Azadi e 1857". You see, at the height of British Raj (the name of the colonial government of India under the monarch of England), there were only one thousand British military officers in India. These one thousands officers from the rank of General to lieutenant ruled the whole of India (todays' India, Pakistan and Bangladesh). The rest of British army was actually made up of Indian soldiers who took their orders from British officers. This Indian army had been created by British government, based on the ethnicity, race and caste of Indians. For example British army would almost never hire a Brahman (an upper Hindu caste) because they were seen as too proud and unruly. They would hire say Punjabi Sikh, because they were seen docile yet brave enough.
But because of a multitude of factors from nationalism to freedom seeking feelings of Indians, a rebellion happened in the army of British Raj among these ordinary soldiers which were called "Sepoy", which is Anglicized of Farsi's Sepahi, meaning soldier. This rebellion spread throughout India and went beyond the barracks into civilian population, and it was nearly successful, threatening to wipe out the British presence in South Asia with certain massacre of all British people living luxurious lives there. But the bravery of British officers, their iron command system and the resolute will of the British Generals saved the day. You have to remember that these were not the days of Air support so the British officers were on their own as any help from England would have taken months to arrive probably even a year.
But two things saved the British without which the locals would have over-run them, no matter the bravery of British officer core. One was the railway that British had built at great cost, which then allowed the movement of loyal British troops and thus giving them mobility to mass troops and encircle the mutineers. And the second was the recent invention of telegraph, which was the top most technology of its time and that British Raj had also implemented it throughout India at great cost just before 1857. This allowed faster information processing by British military command than the leaders of mutiny were capable of coping with. The mutiny failed, at great human cost. But British learned a lesson. The greatest lesson that a colonial power can ever learn. That is to rule over a colony effectively, the most precious tools are socio-political tools. So they implemented alot of these in the days after this mutiny from categorizing the people of subcontinent into loyal feudals who were bestowed with land, power and money/disallowing education, land and wealth for disloyal tribes to more darker methods such as religious manipulations.
After this incident, Hindus were prioritized to receive secular education and were increasingly hired in bureaucracy of British Raj. Then a vast university sized, Sunni learning center was built, by British civil engineers to teach Sunnis. This university is located in Deoband, and Reza Shah's Tehran University or Amir Kabir's Dar-ul-Fonon dwarf in comparison to it both in beauty and massiveness. Out of this place a brand of Sunnism came out that is called deobandi. During the British Raj, this place used to take Muslim students from all over India, with fully paid scholarship for its several years of study (its policy was zero fee). It was a boarding university, meaning that during the time of the study, the pupil was fully committed, living on university campus and following a grilling and no nonsense schedule of studies. When these scholars were sent back to their villages and cities throughout India, they were appointed "Imams" to mosques and received salaries and food rations from the nearby British army cantonment.
These deobandis were the most loyal subjects that British Raj had among Muslim population of India. They pacified the population, and issued fatwas favorable to British Raj. To the extent that when the British government decided to breakup the British Raj and partition India, the deobandis were the only group in India which opposed it. They preferred to remain British subjects. When they saw that the die is cast and British were about to leave, they opposed the creation of Pakistan, preferring Hindu rule. But British abandoned them and created Pakistan over their objections.
When Pakistan was built, understandably, there was little sympathy for deobandis in this new state. They were almost seen as traitors and they were kept at fringes of political and military power of the new state. This changed during the Bengal uprising. During that uprising the Pakistan army was left alone fighting its own population. The only group that offered help to kill Bengalis was the deobandis. This was their chance to prove that they were "patriotic" Pakistanis. But these efforts failed and Pakistan partitioned in 1971. When West Pakistan became today's Pakistan, they were a defeated and humiliated nation. The political and military elite of Pakistan were in search of giving a new meaning to the demoralized nation of Pakistan. This new version came in the form of a harder Utopian Islam, predominantly deobandi version. Deobandis offered their services to Pakistan's military to unify the broken nation. This almost reached epic proportion under General Zia-ul-Haq's rule who elevated the deobandis from the fringes of political power into the center of the nations power politics. He needed them for his secret war that he was waging on Soviet Union in Afghanistan on the order of United States. In order to make deobandi even more hardcore and capable of withstanding Soviet military, Wahabi/Salafi preachers were imported from Saudi Arabia and these preachers upgraded the deobandis into a monstrous war ideology, which was fiercely anti-communist and anti-Shia. I guess you can figure it out yourself why.
After the Soviet withdrawal, Pakistan thought that it could use this same ideology to take Kashmir from India. But the Indian army in Kashmir did not budge as the Soviet military had in Afghanistan. During this time, a cold war of sorts also happened between Pakistan and Iran each supporting opposite groups in Afghanistan which resulted in Iranian diplomats being hanged in front of Iranian embassy when Taleban took over the embassy. Taleban were the ultimate deobandi force that ever came to existence. For a short while. Until, 9/11 happened. The monster had gone the full circle, hitting New York.
The rest you must know well. US went in to Afghanistan promising to hunt down each one of them "dead or alive". Pakistan till 2008 tried its best to atleast partially protect Taleban elements for later use in Afghanistan/Kashmir. But then the monster again went full circle and had started to hit Pakistan. Still Pakistan tried to protect them, since this ideology had become so central to "unity" of Pakistan and its strategic power, believing that this is just a misunderstanding and the Taleban will soon realize that, Pakistan is their master. But by 2013, it became clear in upper echelon of Pakistan's military structure that this was not a misunderstanding anymore and that Taleban had truly gone full circle, so a plan was put in motion for their complete termination despite strenuous objections of deobandis. Whether Pakistan army will ever be able to finish them is up for debate. But even if they do, new groups will emerge. Since the ideology and sympathies for this ideology is deep rooted in Pakistan's society now.
Now with this history in our hand, you will have the minimum requirement to understand the answer to your question. First of all, you should not underestimate the dark desires of humans, specially those arising from hatred and sense of being back-stabbed. From 1970, Pakistani army has been buddy buddy with this ideology and posing as its true friend. When in 2007, Pakistan army decided that it has had enough of deobandi friendship and attacked their flagship mosque in Islamabad as a warning to deobandis that their special relationship was over, the deobandis felt they had been betrayed and back-stabbed by Pakistan. Since deobandis always saw that Pakistan army eventually some day will become a deobandi army. It was too much for them. It was the second time that they were being betrayed. First by the British and now by Pakistan. So they declared war on Pakistan army.
These kids are just the latest causality of this war. A war that is going on in almost every territory of Pakistan nowadays. The reason, that the kids were targeted is rather technical. You see, Pakistan army is quite a powerful army and relatively well equipped, so taking it head-on is suicidal with no tactical benefit. But killing the children of Pakistan army officers and their teacher wives, drives the message right into the heart of Pakistan army. So attacking a school that caters to the children of personnel of Pakistan army becomes their plan. The choice of target is of course, inhuman and despicable but from the view point of deobandis who practice Takfirism, it is acceptable, since they sincerely believe that they are killing kafer, their wives and their illicitly begotten zena-zadeh children. Their enemies. From their ideology's point of view, Pakistan army has become mortad and thus a fair game along with their families.
Deobandis are searching for an identity, they never had. For a religion, they never had. For a country they never had. For a Utopia that is never possible. They were just a tool. Created and used. Who and for what purpose if at all, they are now being used, is a matter for future historians to ponder over their cup of coffee.
And rest assured, this is not the first or the last tragedy in human history. Take the example of female Chinese and Korean children who were used as sex slaves by Japanese army during the World War II. Each had to cater near to couple of hundred men each day. From morning to night, the soldiers were standing in line, and these little girls used to have a small break for lunch only (usually 10 minutes). Refusal meant torture to death or a quick dispatch to the dreaded and horrifying Unit 731 of Japanese Army for the termination as a test subject. After the war those who survived had told their liberators that they had lost all feelings, emotions, humanity and everything else. This is what happens when there is no religion. And that is what happens when we have "religion".
Karma hamisheh hast, Iran ham belakhareh yek rouzi in hameh kesaafat kaari hayi ke anjam mideh, behesh barmigardeh 
, for real? 
