Why does God let people kill each other? because He already kill us all, what is the difference between dying in a bed, in a war or by cancer? it's the same death.
We are born with zero information and therefore God is not responsible for what we learn and what we choose to do.
Now imagine when we were young stealing money/chocolate/etc from our mothers, or when we had to lie, did God have to intervene and punish you? Or are you still young and you are learning and need another chance? There is no doubt that you will reject the punishment and will demand an extension of the exam period.
In the exam, the teacher does not interfere with what the student does, but leaves him to the end of the exam period and holds him accountable, as well as God does, there is no sense to hold the student accountable in the middle of the exam (the earth).
God sometimes sends people to other people to kill them, yes, this is normal because God kills us with many enemies, such as cancer, viruses, and aging, not just because of humans. The world is a small hell, so that man may know that God is capable of creating more evil than the world, which is hell.
now, the important question is why we die? we die because we are just in an examen, earth is a school not the house. we die to leave place to others, so they can pass the examen like us, because the earth cannot bear the immortality of man, it is too small for that. The last man to enter Paradise will have what equal to the earth twice! so imagine what the first man to enter Paradise will have, and how big is the Paradise (the Heaven)...
Ibn Mas'ud reported: Verily the Messenger of Allah said: The last to enter Paradise would be a man who would walk once and stumble once and be burnt by the Fire once. Then when he gets beyond it, he will turn to it and say: Blessed is He Who has saved me from thee. Allah has given me something He has not given to any one of those in earlier or later times. Then a tree would be raised up for him and he will say: O my Lord I bring me near this tree so that I may take shelter in its shade and drink of its water. Allah, the Exalted and Great, would say: O son of Adam, if I grant you this, you will ask Me for something else. He would say: No. my Lord. And he would promise Him that he would not ask for anything else. His Lord would excuse him because He sees what he cannot help desiring; so He would bring him near it, and he would take shelter in its shade and drink of its water.
He (Allah) would say: O son of Adam, what will bring an end to your requests to Me? Will it please you if I give you the whole world and a like one along with it? He will say: O my Lord! art Thou mocking at me, though Thou art the Lord of the worlds? Ibn Mas'ud laughed and asked (the hearers): Why don't you ask me what I am laughing at. They (then) said: Why do you laugh? He said: It is in this way that the Messenger of Allah (may peace be upon him) laughed. They (the companions of the Holy Prophet) asked: Why do you laugh. Messenger of Allah? He said: On account of the laugh of the Lord of the universe, when he ldesirer of Paradise) sai Thou mocking at me though Thou art the Lord of the worlds? He would say: I am not mocking at you, but I have power to do whatever I will.
I cut the hadith to shorten it