Why does Margaret Fuller structure her initial paper as a lawsuit?

Imagine life as a female intellectual in the nineteenth century. Margaret Fuller (Ossoli) was born in Massachusetts and was given an intense classical education by her father, who treated his daughter, academically, as though she was a young boy. Her education started at home but included a short period in her teens where she went away to school. She was urged to learn about fine arts, literature, and history, and she learned to enjoy thinking about and discussing academic topics. Yet, this type of education for females was frowned upon by the average American at this time in history, meaning that she had very few fellow women to discuss her intellectual wonderings with.
Life could be lonely for a female academic in that time. In fact, even though she was surrounded by scholars, including several transcendentalists, such as Ralph Waldo Emerson, she was rarely welcome in academic discourses. Many male scholars found her manner of speaking overly assertive and intense for a woman and were reluctant to invite her into their social circles. It was this widely prevalent disbelief in women's academic and social potential that led Fuller to write "The Great Lawsuit: Man versus Men, Woman versus Women," the precursor to her full-length book, Woman in the Nineteenth Century. This animosity toward women and their intellectual and social potential led Fuller to write her text in the form of a legal lawsuit. 
Fuller's friendship with Emerson was instrumental in developing both of their ideas. Though they did not always agree, they urged one another to consider ideas from new perspectives. Fuller was first acquainted with Emerson when she was invited, by his wife, to the Emersons' home in Concord, Massachusetts. (She was already curious about him, recognizing his growing fame as a local scholar.) From that point on, they maintained a frequent correspondence throughout her life, until she died in a shipwreck off the coast of the United States. This friendship allowed both Margaret Fuller and Ralph Waldo Emerson to grow in their views. It is arguable that Emerson's friendship with Fuller, filled with many intellectual conversations and debates, led him to advocate for women's rights in a couple of speeches, including his speech "Woman," which he gave in 1855.
Fuller was bold, intelligent, and unafraid to be a bit different. This is seen in her personal life as well, as she moved to Europe as a single woman in her thirties, joined the Roman Revolution of 1848, got romantically involved with a Roman Catholic man (though she was Protestant), had a child with him, and later married him. Fuller was a free-thinking woman of the nineteenth century. She challenged the intellectuals around her, including prominent scholars such as Emerson, to think more seriously about the capabilities of women through her words and actions. Her passionate belief in women's abilities to change the world is what led her to structure her literary piece in the form of a lawsuit. As Rebecca Rix, of Reed College, remarked:

"The Great Lawsuit" allowed Fuller to perform in text what she could not in reality: a sermon and a quasi-legal 'case' . . ."

As a woman, Fuller did not have many opportunities to preach the truths of women's capabilities or to present a case for their improved treatment. Since she couldn't actually speak this type of argument, she wrote out her case instead.
https://www.biography.com/writer/margaret-fuller