From the information you have supplied here, you were wrongly denied boarding. Your U.S. visa was sufficient to make the transit:
Information as of 23AUG15 / 0855 UTC
National Syria (SY) /Residence Jordan (JO)
Embarkation Jordan (JO) /Transit Germany (DE)
Destination USA (US)
ALSO CHECK DESTINATION INFORMATION BELOW
TWOV (Transit Without Visa):
Visa required, except for Nationals of Syria holding onward
through Cologne/Bonn (CGN),
Frankfurt (FRA), Munich (MUC), Hamburg (HAM), Dusseldorf (DUS)
or Berlin Tegel (TXL) **AND** meeting one of the following
- holding a valid visa issued by Bulgaria, Canada, Croatia,
Cyprus, Ireland (Rep.), Japan, Romania, USA or United
- WARNING: TWOV is not possible when arriving from a
non-Schengen Member State AND departing to a Schengen Member
I think you should make a complaint to Lufthansa (for the poor customer service) and ask them to reinstate your ticket for travel at your convenience.
Stick to the facts, just say what happened, provide a photocopy of the visa and provide a copy of the email from the embassy saying everything is okay. No need for any emotion. I would not discuss compensation at this stage, but you are possibly entitled to it. Better to seek that later.
In future if this happens I would ask to speak with the Lufthansa Station Manager (who is a Lufthansa employee) rather than just accept what the check-in person says. At outstations, the check-in employees are often local contractors who are not familiar with the airline's rules and they are often poorly trained.