The Luftwaffe did have many strengths. They had excellent (if overmachined and finicky) machines. They started the war with a highly trained air force, and they racked up huge numbers against a surprised and disorganized opponent at the beginning of Barbarossa. However, these numbers actually point to the largest weaknesses of the Luftwaffe, not their strengths.
The Luftwaffe fought longer than any other air force in World War II except Japan and China, whose air war was before 1939 of much lower intensity. As the war went on, they fought increasingly longer odds. As a result, pilots had to fly more and more missions. An Allied pilot would be rotated out of combat; German pilots didn't have that luxury. They flew more sorties, and got more kills, but their odds of survival plummeted.
This points to another major structural flaw in the Luftwaffe: they weren't designed for a long-term air war and the progress of the war prevented them from effectively shifting to meet the needs of one. The Luftwaffe didn't have a sizable reserve of trained pilots; their veterans, instead of taking on training duties, stayed in the air and fighting. Combined with increasing casualties and a shortage of aviation fuel, this meant that by the end of 1944 a rookie German pilot was flying with less than half of the 300 training hours logged by his Allied opponents.
In short: The best Allied pilots retired from combat to train more pilots. A much higher proportion of German pilots had to stay in the fight, and Germany's fight lasted much longer.
There have been several discussions on this topic in the past - one which you may find of interest can be found here, courtesy of /u/ChristianMunich and /u/DBHT14.
To summarise, there were a number of factors at play. Foremost among them were the following:
The Luftwaffe's kill-tracking system often served to exaggerate the kills scored by pilots, as 'shared' kills were disproportionately attirbuted to 'ace' pilots.
The Luftwaffe's considerable qualitative edge in training during the earlier years of the war - particularly against the Red Airforce during the opening period of Operation Barbarossa, but also initially against the Western allies in some theatres.
The Luftwaffe's tendency to keep 'ace' pilots on active combat duty until they were killed, as compared with the allied habit of reassigning their best pilots as instructors.
The above contributed to a situation where the Luftwaffe's 'aces' were far more capable than the average allied pilot, but where the average allied pilot was far more capable than the average Luftwaffe pilot. As the war progressed, the Luftwaffe's qualitative edge was eroded and with the exception of 'aces,' Luftwaffe pilots eventually suffered from being far less experienced than most allied pilots. As such, the imposing kill-counts of the Luftwaffe's 'aces' are unrepresentative of the increasingly ineffectual state of the Luftwaffe during the latter half of World War Two.
I would link to another comment of me from a smiliar thread. The gist of it is that some German pilots heavily outclassed pilots of others nations due to a variety of factors. Thats doesn't neccessarily mean the average German pilot was "better" than the average American or British pilot.