Keller's Learn to Read Latin says
virtis, virtutis f. is an abstract noun formed by the addition of the suffix -tis to the stem of the noun vir. Its specific sense is thus "manliness" or “courage,” but it also may refer more generally to any intellectual or moral "excellence" or “virtue.”
Why is virtis a feminine noun, when it can mean "manliness"?
For about the same reason German "Mädchen" is of the neuter gender. The endings of the noun in a gendered language (like the German diminutive ending "-chen") play a much greater role in determining the gender of a noun than the meaning does. Third-declension abstract nouns formed with the endings "-tus", "-tis" and "-tas" are predominantly feminine, so "vir-tis" is feminine. So is the Serbo-Croatian word "muževnost" meaning "manliness".
