If there's on thing that Wollstonecraft believes in, it's the power of Reason. She loves Reason so much that she even spells it with a capital "R." So it makes sense that she uses the most rational tone she can when putting forward her arguments for women's rights.
As she states in her third chapter, "Let not men in the pride of power, use the same arguments that tyrannic kings and venal ministers have used, and fallaciously assert that woman ought to be subjected because she has always been so" (3.23). Wollstonecraft also associates justice with Reason, and she thinks that you can't have one without the other. This makes sense: when you think about the language of the justice system, you realize that there are phrases like "beyond a reasonable doubt" all over the place. Perfect justice is based on perfect reason (ideally).
When Wollstonecraft talks about morality and goodness, she's not talking about being nice to baby animals. After all, being nice to baby animals is easy, because of the squee! factor. In order to be morally good, you have to employ Reason and a sense of justice. And so, Wollstonecraft uses a justice-seeking tone in her argumentation.
This is extra-clever when you think about the time at which A Vindication of the Rights of Woman was written. The spirit of revolution was in the air, and part of the whole revolution-deal was the desire for justice: no taxation without representation, for example, and the desire to not be starving while Marie Antoinette stuffed her face with bon-bons.