Lose no sleep over this one. An “annulment” merely declares, after a judicial process of the Church, that a marriage which had the appearance and presumption of validity turned out to be invalid from the very beginning. Here, neither the appearance nor the presumption of validity is afforded to any so called “marriage” between persons of the same sex, even if civilly sanctioned.
Marriage by its nature as instituted by God can only exist between a man and woman according to the constant teaching of the Church. This is a matter not merely of ecclesiastical (Church) law but of divine law. While the state can regulate certain civil effects regarding matrimony, the Church does not recognize any validity to social redefinitions of marriage contrary to divine law.
That marriage is constituted by man and woman is reflected in canon 1055§1, among many other places: “The matrimonial covenant, by which a man and a woman establish between themselves a partnership of the whole of life, which is ordered by its nature toward the good of the spouses and the procreation and education of offspring, has been raised by Christ the Lord to the dignity of a sacrament between the baptized.”
Canon 1096 sets up the presumption that after puberty, people are “not ignorant that marriage is a permanent partnership between a man and a woman ordered to the procreation and education of offspring by means of some sexual cooperation.”