Because the Allies and the Luftwaffe/Japanese had different systems for their pilots. When an US ace serves up his tour of duty, he is rotated back stateside to train new pilots and test new airplanes being designed and such. German aces on the other hand are kept on the front lines until they die, so what you have are some very exceptional German aces who are kept on the front lines and rake up the kills while American aces who had the same potential are sent back to improve the quality of the air force as a whole.

A variety of reasons.

When World War 2 broke out the German Luftwaffe was one most technological advanced and best trained air forces. In contrast to air forces of other nations, Germany was able to get valuable experience during the Spanish civil war, a time when many pre war theories were put to the test and redefined. Then again German pilots were able to gain experience over Poland with far superior machines. This combination of starting factors allowed for an advantagous position when it came to fighting the Armée de l'air, RAF and Red Airforce.

From here on several factors allowed for those tallies. Most of the claims were made on the Eastern Front. Several advantages on the side of the Luftwaffe amplified the already significant experience gap. At this point many German pilots had flown many combat missions and were also highly motivated due to the past successes of the Wehrmacht. When Germany struck the Soviet Union the Red Airforce was as unprepared as the ground troops which led to disastrous outcomes of the early air battles. German pilots started reporting many claims. Like said before this obviously again increased the experience and skill of the German pilots while in the same time decreasing the average skill of the Russian pilots who now were often rookies pressed into service. While the foundation for those "experten" was layed pre war and in the early stages the full effect was seen when German pilots kept gaining experience against unprepared pilots who flew inferior machines led by inferior officers.

At this point another important factor comes into play. Most pilots would not be rotated to other functions and kept flying until they died or were unable to fly. Some were pulled out of the units and got other positions but the overall percentage is small. At first pilots who rose to notable fame were often prohibited to keep flying because it was feared their deaths would be serious blows to the moral.

Pilots who kept flying against inferior foes and plenty of targets. This simply created some vastly superior pilots.

Their is a general focus on the Eastern Front when this topic gets discussed. While most of the fighter to fighter combat was happening on the Eastern Front there are several German pilots who had comparable success against Western Allies with Hans-Joachim Marseille being the most prominent.

Jagdgeschwader 27, the unit which fought in North Africa against the Desert Airforce shows that while the above mentioned factors were important there was also a noticable skill difference between German squadrons and Western Allies fighter units, at least in early to mid war. Jagdgeschwader 27 was heavily "outscoring" the British fighter units. Hans-Joachmin Marseille claimed about 150. The unit had only short combat in eastern europe.

The North Afirca theather is unique since fighter to fighter combat was very common. Especially in late war over Germany the missions for both side were very asymtrical. Here the German unit, while being outnumbered, showed a very significant superiority over the British unit when it came to the ability to destroy enemy fighters. The JG27 claimed 1,166 aircraft ( some go up to 1300) in the campaign while only losing a fraction of that. Important is to mention that most of these claims were indeed fighter aircraft. Those claims like all claims are higher than the actual number but those are hard to establish. Thorough research on Hans-Joachim Marseille showed that about 65-70 percent of his claims were cross referenced with available data. It should be noted that cross referencing German claims with British records is hard since British unit logs are hard to come by and are sometimes missing. There isn't even a definitiv number on aircraft losses for North Africa. Several claims of German pilots were disputed for decades until the proper unit log was found. Taking 68% of the before mentioned number we get 792 aircrafts. The Jagdgeschwader lost about 200 machines in aerial combat according to Girbig.

Like said before the mission profile for both air forces was comparable and this discrepancy in lost aircraft indicates either a tactical gap a skill gap or a mix of both. Either way an important part of getting such high tallies was simply being better at shooting down aircraft than the enemy.

This all boils down to German pilots getting a headstart and being trained on very good aircraft with state of the art tactics. Those pilots were then able to gain more and more experience against a weaker opponent who also had a lot of aircraft and provided many targets. Those extremely skilled pilots would now keep flying until they die or the war ends. The word extremely is used on purpose its hard to understand the impact of pilot skill in World War 2. The chance of an average pilot to down one of the best pilots is low. I think it goes without saying but i better say it anways, these pilots were not the majority of the Luftwaffe. Skill level of newer pilots declined due to fuel restrictions which forced the Luftwaffe to cut training hours until trainees got less than 50% of the time their Western Allied counterparts had.

I will try to give an example which shows that for those few pilots it hardly mattered what enemy they faced. Of the 10 pilots with highest claims who also transferred from a different theater to "Defense of the Reich" in late war 2 died, one rammed an enemy aircraft on purpose the other had likely an engine failure. So one of those 10 was possibly killed by enemy fire. Two suffered serious injuries preventing them from flying again during the war. Those ten pilots claimed 123 enemy aircraft amongst them. These are only the claims they made in late war after they transferred towards the Defense of the Reich and only against Western Allies. The skill gap between the average pilot and those pilots was extrem. In those +100 engagements between Allied pilots and those ten ace pilots, US/RAF pilots managed to down two aircraft maybe three. This has to be seen in the context of late war situation where German pilots would hunt bombers and try to ignore fighters. The tally of 123 includes many bombers. By just hunting for enemy fighters this tally would certainly be far higher.

Christer Bergstrom: "Barbarossa: The Air Battle July-December 1941"

Werner Girbig: "Jagdgeschwader27"

John Weal: "Jagdgeschwader 27 'Afrika'"

Edit: I should mention that several topics here are ignored because they have no relevance for the question op asked. This post doesn't discuss what the implication of the above mentioned factors are on the overall performance of the Luftwaffe. OP asked why some pilots had such high claim tallies and i explained why. Overall strategic consideration are also not discussed. Furthermore the debate about claims will always arise, while there is no doub thatt the tallies are higher than the actual number but this is common for every airforce. Some "historians" like Dimitri Khazanov tried to discredit those records with "soviet archives" but got already callout and and debunked.

I wanted to talk a bit more in general about the inaccuracy at large of all nations kill claiming in WW2. Others have touched on it, but in general if your squadron thought the evidence was strong enough to award a kill then you got the kill, be it from a witness in the air or ground, or maybe gun cam footage.

Germany as I also understand it also did not award "partial" kills, so where a US pilot might get 1/3 of a kill with two other pilots, only one German pilot would be given the full kill, you can see how while not large initially that could add up over time to double down on the other factors expanded on below.

Now on to how exaggerated kill counts could get. I will illustrate one example from the Battle of Midway. Now during the attack on the Japanese Carrier task force one of the US fighter squadrons was led by LCDR Jimmy Thatch who was going to test out the new tactic he had developed to allow the Wildcat to protect itself against the Zero, and tested it out with his 2 wingmen that were able to stay with him.

Eventually termed the "Thatch Weave" it basically boiled down to having two elements turn towards each other whenever one had an enemy on their tail.

During this running series of weaves a total of almost 20 Zeros made passes at the trio, claiming 5 Wildcat kills, when in actuality just 1 was shot down. the US pilots for their effort did claim 3 kills which Japanese sources mostly corroborate though obviously the magnitude of the defeat makes accounting who was lost when tough.

Hopefully that makes it easy to see how it is to slowly inflate kills, when you see an enemy plane dive away trailing smoke and another saw it, then it becomes easier to claim the kill, then if that plane survives and rejoins the fight you aren't going to really be able to tell it is the same one so all of a sudden it might get credited as a different kill 2, 3 , 4 times and might not ever have been shot down.

I would like to point you to this, where a bunch of flaired users discussed it.