Final answer:
The Impressionists were considered radicals because they broke the rules of traditional academic painting and focused on capturing light and color in their work. Their departure from traditional standards led to criticism and accusations of quackery and immorality.
Step-by-step explanation:
The Impressionists were derided as dangerous radicals or "Intransigents" because they violated the rules of academic painting in 19th century France. The Académie des Beaux-Arts, which dominated French art at the time, valued traditional subjects, conservative colors, and realistic details.
The Impressionists, on the other hand, focused on capturing the effects of light and color in their paintings, using visible brushstrokes and unblended colors. Their departure from traditional standards and rejection of the Salon led to criticism and accusations of quackery, immorality, and anarchy.