A Vindication of the Rights of Woman is a pretty no-nonsense title for a book. The word vindication in Wollstonecraft's title refers to "show(ing) that something that has been criticized or doubted is correct, true, or reasonable."
So Wollstonecraft is saying "Hey. You doubt that women's rights are reasonable? I'm here to show you just how freaking reasonable they are. Listen up, y'all."
Wollstonecraft wrote this book to stand up to all of the men of her time who thought that a woman's place was in the kitchen and that women had feeble brains that couldn't deal with tough manly-man stuff like philosophical discourse. She adopted the (sometimes difficult, not gonna lie) language of rational philosophy to show these men that she could outwit them at their own game. This means she is able to make her point in two ways: 1) through the arguments she makes, and 2) in the way she articulates these arguments.