My best guess is for two reasons: 1) He can. 2) It drives the opposition batshit insane:
The president who campaigned for a more “open government” and “full disclosure” will not unseal his medical records, his school records, his birth records or his passport records. He will not release his Harvard records, his Columbia College records, or his Occidental College records — he will not even release his Columbia College thesis. All his legislative records from the Illinois State Senate are missing and he claims his scheduling records during those State Senate years are lost as well. In addition, no one can find his school records for the elite K-12 college prep school, Punahou School, he attended in Hawaii.
The whacky public image of the “Birthers” continues to do much damage to more rational criticism of Barack Obama’s administration. Whether there is “fire” to go along with all the breathlessly described “smoke”, it’s taking lots of attention away from the actual policies and actions of the current president, and tarring-by-association those who do criticize. That’s enough of a political win that Obama would be very foolish to do anything to calm them down by releasing these documents.