There are two related reasons for Demosthenes' objection to the expanding conquest of the Macedonian Empire. First, Demosthenes was patriotic to his city, their alliance with other Greek city-states, and the Greek culture. Phillip II of Macedon's advances into Southern Greece were a serious threat which was at first taken too lightly by many Athenians, who failed to recognize Macedon as a formidable foe. Traditional enemies such as Persia held the public attention. Demosthenes recognized the danger Phillip II represented, and sought to warn his fellow Athenians to prepare for the Macedonian conqueror's advances, seeking increases for the Theoric Fund and an increase in military preparedness.
Over the next decade and more, Phillip II would prove his military competence, and Demosthenes would see his ability, his ruling style, and his cultural norms. None would prove reassuring to the Athenian orator and statesman. This ultimately came down to his loyalty to his culture. He was proud of Greek culture, and shared the common discomfort with "barbarian" nations. The real heart of his argument that Phillip's rule would be worse than Sparta's lay in this: Sparta was Greek, politically and culturally. While often seen as the least "civilized" of Greek city-states, it remained Greek in its culture and ideals.
Macedonia was, in the eyes of the Greeks, alien, with a culture they saw as quite literally barbaric. To be dominated by rough and ready Sparta was shameful for one of the great lights of Greek civilization, but to be conquered and ruled by a barbarian was a cultural disaster, both logically difficult and emotionally humiliating.
Conquest by Phillip also threatened the democratic system of the city of Athens--a system Demosthenes treasured and fought to protect. Phillip was a a king and a tyrant. Athens had no place for tyranny. Demosthenes could only fear Phillip, and later Alexander the Great, for the threat they represented to Athenian democracy and Greek cultural dominance.