It doesn't. In fact the Koran says that killing one person is on the same level as genocide. The reason everyone thinks what you typed is because of the extremists. They unfortunately have placed the perception of Islam as a 'jihadist' religion. But Islam does not have any teachings that recommend violence in any way.
But when the forbidden months are past, then fight and slay the Pagans wherever ye find them, and seize them, beleaguer them, and lie in wait for them in every stratagem (of war); but if they repent, and establish regular prayers and practise regular charity, then open the way for them: for Allah is Oft-forgiving, Most Merciful. Ch. 9:5 (at-Tawba)
Then there is:
"2.190. Fight against those who fight against you in the way of Allah, but do not transgress, for Allah does not love transgressors.
2.191. Kill them whenever you confront them and drive them out from where they drove you out. (For though killing is sinful) wrongful persecution is even worse than killing. Do not fight against them near the Holy Mosque unless they fight against you; but if they fight against you kill them, for that is the reward of such unbelievers.
2.192. Then if they desist, know well that Allah is Ever-Forgiving, Most Compassionate.
2.193. Keep on fighting against them until mischief ends and the way prescribed by Allah prevails. But if they desist, then know that hostility is only against the wrong-doers."
It's all about the interpretation and context as taken by the various sects, just like it is in other religions of the world. To deny what it says is just as wrong. It says what it says.
But you will never read where the scripture of the Holy Bible's New Testament authorizes the Christian, follower (disciple) of Jesus Christ, to do those same things as quoted above to others. In fact he said to love your enemies and seek to turn them away from their sins and to forgive them 70 times 7 (infinite). Which is what he did throughout his days on earth and as he was being executed.
Religion is never the answer. Faith in Christ coming from a renewed heart is always the answer.