Basically, you need to understand the fact that Islam is always in a State of War against the Disbelievers. Hence, someone who leaves them, joins the ranks of the Enemy and becomes a Traitor and Turncoat, for which, the sentence is Death.
al Qur'an, Surat ahl e Imran(Family of Imran) 3:110
You are the best nation produced [as an example] for mankind. You enjoin what is right and forbid what is wrong and believe in Allah . If only the People of the Scripture had believed, it would have been better for them. Among them are believers, but most of them are defiantly disobedient.
al Qur'an, Surat Al-Bayyinah(The Clear Proof) 98:6
Indeed, they who disbelieved among the People of the Scripture and the polytheists will be in the fire of Hell, abiding eternally therein. Those are the worst of creatures.
These are just a very few of the actual verses from their own Qur'an where you can see that they are told that they [Muslims] are the Best Nation and all the non-Muslims are "Worst of all Creatures".
Naturally, that is psychological preparation to make them loathe all non-Muslims and "see" only all that is bad about them, whether they be true or perceived.
That's why we hear the Muslims always talking about how vile and immoral all non-Muslims are; how the Christians let their women dress provocatively, and how Christian parents allow their sons and daughters to make and act in pornographic movies, and how the Christian parents don't care whom their daughters and sons sleep with and all such preconceived notions that are of their demented thinking which you always hear them spewing everywhere.
Now, if you are preconditioned to see all non-Muslims as these vile and immoral "Worst of all Creatures" by the repetition of these verses and listening to the harangues of your Imam who keeps on and on telling you - "Look at those kaffirs and the way their women expose part of their breast and their legs in those immodest dresses! Wallahi! What foul creatures they be!" 5 times a day; don't you think that they will build up enough Hatred to want to rape these filthy women and kill all of these most foul and vile infidels?
al Qur'an, Surat ahl e Imran(Family of Imran) 3:28
Let not believers take disbelievers as allies rather than believers. And whoever [of you] does that has nothing with Allah , except when taking precaution against them in prudence. And Allah warns you of Himself, and to Allah is the [final] destination.
Allah commands Muslims to never befriend a non-Muslim nor take him for an ally and only deceive those foul and vile "worst of all creatures" - the Disbelievers, with words that do not come from their hearts.
al Qur'an, Surat At-Tawbah(The Repentance) 9:123
O you who have believed, fight those adjacent to you of the disbelievers and let them find in you harshness. And know that Allah is with the righteous.
al Qur'an, Surat Muhammad, 47:4
So when you meet those who disbelieve, strike their necks until when you have inflicted slaughter upon them, then secure their bonds, and either confer favor afterward or ransom them until the war lays down its burdens. That is the command. And if Allah had willed, He could have taken vengeance upon them Himself, but He ordered armed struggle to test you by means of others. And those who are killed in the cause of Allah - never will He waste their deeds.
Allah commands them to fight the non-believers with whatever weapons of deceit and actual killing to rid the World of such despicable "worst of all creatures" - these filthy immoral, abominations to Allah and start by finishing off your neighbor and then moving on to the next till there are no more non-Muslims left in the World to offend Allah and His Laws. And you see this commandment of Allah, which is also in the Surat at Tawbah - to kill the Disbelievers and wage War against them, repeated in many other Chapters like the Surat Muhammad, Chapter 47 of the Qur'an.
You see, they look upon themselves as Warriors of Allah and Heroes in the Unending War to cleanse the World of the filthy, immoral, lowest scum "Worst of all Creatures" as they really see all of us as. And one who leaves their fold and joins, by default, the Enemy Camp is to be killed.