Those who comply with society's dictates are those of "sense," while individuals who think for themselves are considered "mad" as they are a threat to the compliance of the majority, who follow the dictates of society.
Emily Dickinson's paradoxical statement that "Much Madness is Divinest Sense" is predicated upon the concept of individualism in opposition to what Ralph Waldo Emerson, in his essay "Self-Reliance," called "the joint-stock company" of society. Those individuals who think for themselves are labeled as mad or shunned because they threaten the status quo.
Assent--and you are sane--
Demur--you're straightway dangerous--
And handled with a Chain
One real-life example of this reactive action by society upon someone who dissents is in the biography of the poet Ezra Pound. During World War II, Pound lived in Italy for a time, and he spoke out against the American military and expressed anti-semitic views. Consequently, he was charged with treason, but his case was worked out so that he could be committed to a mental institution.
In Dickinson's own life, her father's Calvinistic insistence upon perfection and compliance conflicted with Emily's clear-eyed scrutiny of the world; as a result, she grew more and more reclusive, feeling "straightway dangerous" as she rejected the rigidity of her father and the insanity of following the dictates of society.