I'm going to chalk this up to President-bashing, which has been gaining increased momentum over the past decade. The likelihood of the President of the United States (Whom is ALWAYS shown in the world's eye) would wear the American Flag pin upside-down, which is disrespectful of our country in almost every way. He has teams of people to look over his appearance before stepping out and into the public's view.

I'm going to chalk this up to President-bashing, which has been gaining increased momentum over the past decade. The likelihood that the President of the United States (who is ALWAYS shown in the world's eye) would wear the American Flag pin upside-down, which is disrespectful of our country in almost every way, is low. He has teams of people to look over his appearance before stepping out and into the public's view.

EDIT: I have a few more references and points to make (For quality assurance, of course);

First, on the unverified Wikipedia page:

Below are some of the most common reasons for discharge:

• Expiration of Term of Service (ETS)
• Reaching the maximum age limit
• High Year Tenure (reaching the maximum allowable time-in-grade, and not selected for promotion)
• Disability, Dependency, or Hardship
• Pregnancy/Parenthood
• Personality Disorder
• Condition not a disability
• Physical or Mental Conditions that interfere with military service resulting in being placed on the Temporary or Permanent
• Disability Retirement Lists
• Convenience of The Government/Secretarial Authority (voluntary redundancy due to funding cutbacks, for example)
• Unsuitability
• Misconduct - Minor Disciplinary Infractions
• Misconduct - Drug Abuse with and without administrative review board
• Misconduct - Commission of a serious offense
• Entry-Level Performance and Conduct
• Resignation (available to officers only)
• Reduction in Force (RIF)
• UnCharacterized if discharged within the first 180 days of service and no misconduct found in service members record
• Punitive Discharges - Bad Conduct Discharge issued by either Special Court Martial or General Court Martial only. Dishonorable
• Discharge issued by a General Court Martial only

This all seems very vague, though what isn't covered here is likely covered underneath an Administrative Separation Board for review.

Second, this page goes over the process pretty extensively, specifically

Once the commander receives the attachments from the respondent, he/she determines whether or not to proceed with the discharge proceedings. If the commander elects to proceed an administrative discharge board is convened (if required). If the board is not required, the commander forwards the package to the approval authority (usually the installation commander) for final approval or disapproval.

The President would certainly have to go through the proper military channels in order to separate a service member.