"Miles's whole title to independence, the rights of his sex and situation"

From feudal times until 1925, the rule of primogeniture ensured that a deceased parent’s wealth, estate and title were passed on to the eldest male child, even in the absence of a will. This was intended to ensure that such assets remained undivided and in the possession of the family. Other male children would receive financial support from the heir, but girls were expected to rely on the dowries they received upon marriage.

Though Miles is currently under the legal guardianship of his uncle, he will (or rather, would) come into possession of his parents' assets and possibly Bly as well upon turning 21, the age of inheritance. The governess, therefore, perceives him to some degree as her incipient master.