Final answer:
Socrates was viewed as a threat to Athens' democratic society due to his critical questioning methods, which challenged the foundations of democracy and embarrassed influential citizens, as well as his perceived connections to undemocratic elements such as the Thirty Tyrants.
Step-by-step explanation:
Socrates was considered a threat to authorities in democratic Athens for several reasons. His method of questioning, known as the dialectic method, embarrassed and challenged many of the city's prominent citizens, including poets, statesmen, and artisans, by revealing their lack of knowledge on subjects they claimed to understand. Socrates's approach to teaching and his association with individuals from various backgrounds, including future tyrants, elicited suspicion and distrust among Athenians. Moreover, his philosophical inquiries often questioned the very principles of democracy, suggesting that decisions made by the majority were not necessarily based on wisdom or an absolute standard of truth. These actions and his association with the Thirty Tyrants, even if not directly supportive of their regime, left him vulnerable to charges of corrupting the youth and impiety, leading to his trial and execution in 399 BCE, which Plato documented in dialogues like the Apologia.