not wanting to get into writing a book on emergencies, each situation is different. some can’t for whatever reason say the word emergency, others don’t want to. the freaking answer was to the statement that only the freaking pilot can declare. from the ATC handbook:
EMERGENCY DETERMINATIONS
An emergency can be either a Distress or an Urgency condition as defined in the “Pilot/Controller Glossary.”
A pilot who encounters a Distress condition should declare an emergency by beginning the initial communication with the word “Mayday,” preferably repeated three times. For an Urgency condition, the word “Pan‐Pan” should be used in the same manner.
If the words “Mayday” or “Pan-Pan” are not used but you believe an emergency or an urgent situation exists, handle it as though it were an emergency.
Because of the infinite variety of possible emergency situations, specific procedures cannot be prescribed. However, when you believe an emergency exists or is imminent, select and pursue a course of action which appears to be most appropriate under the circumstances and which most nearly conforms to the instructions in this manual.
didn’t write it, argue away if you feel you must
Not arguing with the definition of the term, but ATC does not declare emergencies for aircraft. Your reference doesn’t state they declare emergencies for aircraft. Not arguing, stating facts.