Is he his dad or mom? Does it have to do with Kabuto? Is Kabuto his dad since Orochimaru can switch bodies? Did Orochimaru turn to a girl and have Mitsuki?
Mitsuki was created as a synthetic human by Orochimaru. It has been revealed in Boruto: Naruto the Movie that, Mitsuki is Orochimaru's son.
In the movie, Boruto questions Mitsuki about his parentage to which Mitsuki replies that he is the son of Orochimaru. Sarada is surprised by the same and asks whether Orochimaru happens to be his father or Mother while Boruto asks who Orochimaru is, and Mitsuki replies that it doesn't matter which leaves Boruto and Sarada confused.
Mitsuki is a synthetic human who was developed by the scientific powers of Orochimaru.
Mitsuki does question Orochimaru about this. Orochimaru states that he is his parent, he doesn't reveal the gender.
It is shown in the anime that Suigetsu helps Orochimaru create and help form Mitsuki.
Source: Episode 39 "The Path Lit By The Full Moon"