[PHXFlyer]

From Delta.com:

Safety Guidelines and Procedures

Here are our safety guidelines and procedures for making sure that your child has the best flying experience possible:
General Guidelines

• Children 15–17 are not required to have unaccompanied service but we will provide it when requested.

You requested this service. It wasn't required. Subsequently you complained about the restrictions of a service you requested. Moving on.

• An unaccompanied child can not be booked on the last connecting flight of the evening. This is to prevent the need for an overnight stay in a hotel. Contact Reservation Sales before you book here at delta.com if you have questions about connecting flights.

There it is in black and white. Furthermore...

Preparing for Travel

• Plan for any necessary medical needs. We cannot administer medicine to children flying alone. If your child is unable to give herself medication, other travel arrangements must be made.

So your arguments about her medical needs were already addressed. Of course you probably never bothered to read any of this. Anyway,

At the Airport

• Bring your child to the airport ticket counter for check-in. A ticketing representative will:
  • Verify contact information.
  • Collect appropriate fees.
  • Issue a red and white striped identification button that must be worn at all times.
  • Verify that your child has proper proof of citizenship and other necessary documents if traveling internationally.
  • Rebook an alternate flight if it appears bad weather may divert the flight from its final destination.
• One (only one) parent or guardian must accompany children ages 5–14 to the departure gate and must:
  • Obtain proper documentation from the Delta Ticket Counter to pass through airport security checkpoints.
  • Remain in the gate area until the plane takes off.

It's more than obvious now that weather was an issue so they re-booked her on a flight the next day. So the next time you go off calling someone a jerk or an idiot realize that just because that jerk/idiot isn't telling you what you want to hear (that includes myself and the Delta agents you spoke with) that the jerk/idiot you're talking to might just be smarter than you and realize that the rules and policies are there for a reason. In this case those rules and policies exist for the safety and well being of your child!