The status of a mother determining the status of the child became the defining factor for legal status of enslaved and free African people. Originally, genocidal hierarchies imposed by the colonial state were defined not by the color of one's skin or the status of a mother but by the religion of a person. African people and indigenous people were considered "heathens", and as such, were considered sub-human and fair targets for genocidal campaigns and enslavement. As christian militias began forcing indigenous people to convert to christianity under threat of murder, and as slave owners decided to forcefully convert enslaved African people, the division of peoples based upon religious factors became an ineffective way for the colonial state and slave owners to maintain control.
Additionally, the colonial state realized that enslaved African people and indentured Europeans were forming personal and romantic relationships as they found themselves much more in common with each other than the colonial masters. As such, the state sought to use divide-and-conquer tactics to make interracial uprisings and solidarity much more difficult.
During the mid-1600s, a series of horrific laws were passed in the colonies that banned interracial relationships, barred black people (free or enslaved) from owning firearms, allowed black women to become a literal taxable good, declared that any child of an enslaved black woman inherits slavery, stopped conversion to christianity as a means of obtaining freedom, and legalized murdering black people for "resisting" slave owners or slave catchers. The above listed laws are just a handful of the many laws passed within this time period that created the framework of legalized slavery, murder, genocide, and segregation.
While skin color became a defining factor in cementing social hierarchies, many light/white skinned children were born into slavery due to white slave owners raping enslaved black women. Rather than put the spotlight on white men who were clearly raping black women, the colonial state determined that the legal status of black women would always determine the status of the child. Thus, in addition to committing the horrific act of owning another person, white slave owning men could also rape black women with impunity.