They say: The inhabitants of F.Y.R.O.M. speak what was once known as the ancient Macedonian language.
The Truth is: What is spoken in the Vardar Banovina region today is a Slavic variation of Bulgarian. This language evolved to what it is today after two Greek brothers, missionaries of Christianity from Thessaloniki; Cyril and Methodius (who later were named saints); brought Christianity to the Slavs in about 855, and introduced the Glagolic (First version of Cyrillic) alphabet in order to be able to translate (the Slavs were lacking a form of written language at the time) Greek Christian text into Slavonic (Old Bulgarian).
They say: Ancient Macedonians were not Hellenes because they used to war and destroy Hellenic cities.
The Truth is: Due to the geographical character of Greece and the lack of physical continuation between the City States, often political and/or financial friction was created between the City States resulting to skirmishes (A very common way of resolving issues at the time) and is far from being proof of Ethnic Identity. However proof of the Hellenic ethnic identity shared by the City States (inclusive of Macedonia) is the fact that all used to unite when in peril, into one military force to fight off invaders (such as the Persians) and drive them outside their lands and territories.
The list of fictitious arguments is endless...
The lighter side of the controversy
On the lighter side of this controversy, it is really humorous to see that even the Vardar Banovina nationalists don't believe their "Macedonian" background claims and they manage to debunk their own arguments to the rest of the world amusement:
The name of Macedonia is an Ethnic Symbol, a symbol that is inherited based on blood line, an inheritance that goes back to the original Macedonian Hellenes, an inheritance that cannot be duplicated, emulated, or acquired through thievery, political pressure, or historical forgery.