In the "300" movie, in the final battle, Why didn't Leonidas kill Xerxes?

Because Leonidas and Xerxes were actual historical figures that have well documented histories. Xerxes lived through the battle.

Also The Battle of Thermopylae is a well-documented event. Taking artistic license, like having a spear graze Xerxes’ face is one thing. Changing historical fact like having Leonidas’ spear kill Xerxes would simply draw laughter from people that know how the battle went.

In the context of the movie only: Leonidas did try to kill Xerxes, but it was a long, difficult throw. The (artistic) tragic part to this is that, if Leonidas had thrown a slight bit softer, the spear would have plunged a few inches lower, and the throw would have gotten Xerxes in the chest (and probably kill him). And so Leonidas dies having missed because he “tried too hard” to get distance on his throw.

The following clip explains why Leonidas knelt (to shed his equipment in a passive manner) as preparation to make a difficult spear shot.

Because Xerxes believed himself to be a god, immortal and immune to physical injury, and his army believed it as well. Leonidas intentionally injures Xerxes, rather than killing him, to serve a major blow to Xerxes' own belief of being a god, and to eventually weaken the resolve in those that follow him and to strengthen the resolve of those that will come to fight the Persians.

If Leonidas had killed Xerxes, there's no guarantee that those that followed him wouldn't make him a martyr and continue the war effort, picking the most zealous leader and moving forward. Leonidas, despite his arrogance, was looking at the long game.

While I agree with other users that the throw was in fact very hard, and that Leonidas pulled an impressive stunt even with that minor injury, I think there's a point in particular that needs to be considered, from a narrative point of view.

The movie is narrated by Dilios, the only Spartan soldier that left the battle. He was specifically asked by Leonidas to leave so that he could tell the story of the battle: his precise mission was to inspire others so that the war could still rage on after Leonidas's defeat.

Dilios is telling the story one year after it took place, as the Greek allied army was going to fight the Persians once more. Xerxes was leading that army too: everybody knew that he lived through the battle of Thermopylae, so it was evident that Leonidas could not manage to take his life.

Also, Dilios left the place before the final showdown happened. He never saw the spear throw, he never saw Xerxes bleed, he never even saw Leonidas die. Speaking from an in-universe perspective, the entire final scene is just a glorification of Leonidas that Dilios completely made up. Dilios was still alive because he had to inspire the Greek people, and he did that fairly well :)

Because it's a spear, manually thrown from a great distance, affected by wind, how well the spear was built, etc. It's not a round fired from a scoped and adjusted sniper rifle on a mounted stand, with a spotter with binoculars.

To hit Xerxes, at all, was a tremendous throw. Even someone shooting a sniper rifle would be unable to shoot with the kind of precision to just graze like that, so clearly, "just" winging him was not intentional. Even though it's fiction, you probably take your suspension of disbelief concerning their prowess with weapons a bit too far.

Leonidas was trying to kill him with an impossible spear throw.... and he almost pulled it off.

Simply, because Xerxes survived that battle. The movie was based on actual events; The Hot Gates existed, the Greeks (Spartans) were betrayed by a resident (Ephialtes) who told the Persians about the path that led behind their lines, and Leonidas died in that battle. These are all historical facts. Why would they have Leonidas kill Xerxes if that didn't actually happen?

Leonidas did not miss the shot. Instead Leonidas did not kill Xerxes because he had to respect the Carnea - the ancient greek festival during which Sparta wages no war (Recall the scene where he goes to talk with Ephors and they consult the Oracle).

If killing Xerxes was the aim, he would have taken the entire army to war but he could not do that as that would be disrespectful to the Carnea. After talking with Ephors, he was disturbed in his palace that night. That's when before their sex scene, his queen told him that he should not think like a king or a husband or a Spartan citizen, but as a free man. As a king he cannot wage a war during Carnea but as a free man he can absolutely take a stroll to stretch his legs and take a few (300) bodyguards with him. And that is exactly what he did - issued no order for taking the army and took a "stroll" up North - towards the Hot Gates. This way Carnea was respected and he too could do something to save Sparta.

Finally, he did not kill Xerxes because that would be an act of war, but he did stamp his wisdom and courage by showing that even the God King can bleed, implying that Spartan king was no less. Not killing Xerxes and stopping after only making him bleed, he let the enemy arrows kill him and the rest of his 300 men. With that he respected Spartan tradition and at the same time also showed that not only the Spartan king did not submit, but also would have made Xerxes and his army bite the dust - had there been a war. In the process he laid down his life for his people and his country.

^{(This answer was provided by @displayname in the comments section. Due to the question being protected, @displayname gave me full permission to post it as an answer. All credit to him/her)}

Because that would have changed history.

While the movie takes creative license, the characters involved were in fact real characters and the movie is based on real events. Killing Xerxes in the movie would be changing the facts about history.

His helmet was stifling, it narrowed his vision, and he must see far.

His shield was heavy, it threw him off balance, and his target is far away.