While it's not directly stated, Mycroft expresses his disapproval of marriage in the story "The Adventure of the Bruce-Partington Plans". When Sherlock mentions the marriage of his friend's daughter, Mycroft responds with, "Marriage is a most dangerous institution. It is an excellent thing for the propagation of the species, but, as a rule, it is distinctly injurious to the individual".
This hints at a general disdain for marriage on Mycroft's part, and as a powerful and influential man, he might prefer the girls in his life remain single and focused on their own lives.