Wollstonecraft writes this book as a first-person narrator. The book is a philosophical treatise, after all, coming from the mind of Ms. Mary W. herself, so the choice makes sense. But don't let the fact that Wollstonecraft's speaking in the first person fool you: it's not always the voice of Wollstonecraft that is speaking.
She's definitely using a philosophical persona for making her arguments. She almost comes across as totally omniscient at some points, since she's relying totally on basic logic instead of her own personal opinions. It's not a fireside chat with Ms. Mary here. This is a freaking philosophical treatise, and if Wollstonecraft is advocating for the rights of women based on their ability to reason then, by golly, she's going to employ some dang reason. She doesn't want to make Vindication sound just like one woman's opinion.
But Wollstonecraft is enough of a diplomat to know that some humanizing is necessary if she wants to fire people up. Occasionally Wollstonecraft drops her philosophical distance and becomes very personal, saying things like, "The very word brings Mrs. Macaulay to my remembrance. The woman of the greatest abilities, undoubtedly, that this country has ever produced" (5.124).
It's this balance between the rational/universal and the highly personal (or omniscience and first person, if we want to use those sweet Lit terms) that makes Vindication such a stirring read. You can see this same blend of the omniscient and personal in a lot of great speeches: check out Martin Luther King's "I Have A Dream" speech for a similar combo.