Originally Posted by Often1

Seems to have followed standard US air carrier policy. This was not a decision of one employee, but rather the Captain who was advised by others. Don't focus on how many drinks you had over the course of the journey, but how your conduct might appear to others.

However framed to OP, the FAA rules (which apply here because DL is a US carrier) are that the passenger is not to be served if "he appears intoxicated." 14 CFR 3-3546.

The FAA rules require that the PIC and the relevant staff complete a written report, so there will already be one on file, whether OP complains or not.

More than likely, DL will commend the Captain and others involved for their actions.

For what it is worth, don't focus on the exact language used. Staff are trained not to directly confront passengers when avoidable. E.g., "I think you're drunk" becomes "you appear to be over the limit" (even though there is no established limit by number of drinks). This also has nothing to do with a "threat." If a threat, OP would have been denied boarding. This had to do with serving booze.