The Germans simply did not have enough aviation fuel to train their pilots, and effectively defend their skies. Romanian crude oil was unsuitable for high-octane avgas, so the Germans relied on hydrogenated coal mixed with tetraethyl lead to produce Avgas in the 90-octane range. In comparison, the RAF started using 100-octane right before the battle of Britain.

Eventually the Americans realized that ball bearing plants weren't the industrial bottleneck they had originally thought, and focused instead on destroying the hydrogenation plants. Within months the Luftwaffe's abilities were significantly degraded.

See this chart: You can see that Germany's production never matched that of the Allies and Soviets.

Even the airfleet they did build suffered from serious deficiencies. First was the lack of a truly effective long-range bomber. That allowed the Soviets to rebuild a massive industrial infrastructure out of range of the Wehrmacht, and it also prevented Germany from doing meaningful damage to British industry and logistics.

The Germans also did not develop a naval bombing force capable of imposing a blockade on Britain or supporting a cross-Channel offensive.

Now go back to that chart. You see that German production took a long time to reach its peak; for several years, low production was caused by an over-emphasis on precisely engineered (but finicky) machines, by weaknesses in Germany's program of industrial coordination, and most of all by the constant shuffling of priorities given scarcity of resources and manpower.

By the time German aircraft production really got underway, it was far too late. The Eastern Front was crumbling and the USAAF was fielding vast numbers of planes from Britain and Italy. The need to hoard scarce fuel for battlefield usage led to a dramatic shortening of training times, as did continuing losses; most of the Luftwaffe's veteran pilots were wounded or killed and therefore could not contribute in the field or as mentors.

Was is that their planes were technically inferior?

At the beginning of the war, the Bf 109 was a cutting edge fighter. It was updated a number of times during the war and was never completely outclassed by Allied fighters, but it was an aging design by the time 1943-44 when the Americans joined the air war in earnest. The FW 190 was introduced during the war and was a close competitor to most Allied fighters. Overall, the German fighters were not outclassed by any wide margin. The Me 262--a jet fighter--was an excellent step forward for the Germans but it was not only introduced too late in too few numbers to make a substantive difference, but the Allies had their own jet fighters that were comparable.

Was it the pilots training?

To an extent. Another post points to fuel shortages that contributed to a lack of training time for German pilots, which is true. However, by the time that this was a problem the trend was already going against Germany.

Was it their strategy?

/u/Prufrock451 is absolutely right to point out that Germany never came close to total Allied war production. Martin Van Creveld has some interesting things to say about wartime aircraft production. Beyond the pure numbers, he examines production as a function of industrial potential.

Taking the period 1940-45 as the best available compromise, we find that, in those six years, the United States produced 309,761 aircraft. Germany built 109,586, the British Empire 143,234, the Soviet Union 147,836, and Japan 74,646. Earlier in this chapter it was estimated that, if America's industrial potential in 1939 stood at 3, then the figures for Germany, the British Empire, the Soviet Union, and Japan were 1.2, 1, 0.8, and 0.5 respectively. Combining the two sets we find that Germany produced somewhat less than its fair share of aircraft. The British Empire produced considerably more, and the USSR many more. Japan, too, produced more than its share. This calculation ignores many factors, including the extent to which the various countries mobilized their resources and the types of aircraft each produced. Still we conclude that, relative to their overall industrial potential, all the main belligerents except Germany built more aircraft than the United States did. (emphasis in original)

Germany attempted to take on the largest industrial powers in the world at the same time. The result was that they were swamped with enemies on two fronts.

RAF defended successfully Britain, why couldn't Luftwaffe do the same?

Even all by themselves, the British outproduced the Luftwaffe when it came to planes during the Battle of Britain. Once the Americans joined the air war in 1943, the Germans could not come anywhere near matching Allied numbers. Even with Germany switching over to a heavy emphasis on fighter production (rather than bombers) for protecting their heartland, the Germans never produced enough fighters to match the Allies.

Now, this isn't to say that the Germans didn't have success on the defensive. The Americans entered the air war over Europe in earnest in 1943. They were convinced that the B-17 would be able to make it to its target and back in daylight without fighter escort. While the Flying Fortress was an excellent bomber, it failed to be able to survive without fighter escort. American losses were unsustainable, and they had to call a break in the bombing to both build up their numbers and to get long-range fighters into the fight.

That is why the Germans ended up losing aerial superiority over Germany. The Allies were able to produce a large number of bombers that obligated the Germans to use their fighters to try to stop the bombing raids. The addition of Allied long-range fighters that could escort the bombers to their targets and back meant that the air war was a war of attrition. Given that the Germans had little in the way of qualitative superiority and were unable to match the quantity of Allied aircraft, they were unable to do anything but mount a valiant defense while being ground down to an ineffective force. The Luftwaffe was unable to mount any effective defense to D-Day because it had been previously destroyed over Germany. Combine the deficit in fighter production with a shortage of pilots, and the Luftwaffe was constantly in decline from 1944 onward.

I think Robert Watson-Watt deserves a bit of credit here, especially at the beginning of the war. His invention of the radar allowed the RAF at the beginning of the war to fight the superior numbers of the Luftwaffe through the Dowding system. According to Stephen Bungay, the RAF had roughly 600 less aircraft than the Luftwaffe. The superior Dowding system allowed the RAF to coordinate their defense extremely well. Knowing, as seen here, immediately when the Germans left the continent to attack, was absolutely invaluable.

Sources for this quick post: "The Most Dangerous Enemy: An Illustrated History of the Battle of Britain," by Stephen Bungay

Chris Trueman's "History Learning Site." About the Author with his credentials here.

Follow up question : Did Germany even have Air Supremacy during the beginning of the war?

In addition to what's already been said I'd like to add that it depends on which theatre your talking about.

In Britain the Luftwaffe were close to victory over the RAF in the Battle of Britain but Hitler changed their orders at the last minute to target industry and civilians, commencing the Blitz which gave the RAF essential time to recover.

In Russia their supply lines were stretched and equipment badly affected by the cold weather with fuel freezing in engine for example.