The taught has two objects: first object is missed (Teaching Quran to whom?), the second object is Quran. This is said Taghdir in Arabic language. There are some possible forms in this Ayah that interpreters mentioned. Here are them:
علم الانسان القرآن
Taught the Quran to man
علم الانس و الجن القرآن
Taught the Quran to man and jinn.
Allamah Tabatabie, one of the greatest interpreters of Quran and writer of interpretation Al-Mizan, preferred the second interpretation and stated:
In this Surah, man and jinn together is subjected several times and if this teaching were merely for humans, It wouldn't be correct to subject man and jinn again and again in later ayahs.
Beside the point, this order of ayahs implies that teaching Quran is the beginning of the count of Allah's blessings. Quran indicates the expression of the paths of happiness, the happiness which is the wish and the purpose of all the seekers, thus placing it ahead of other blessings, and teaching it even ahead of the creation of man and jinn that the Quran has revealed to their teachings.