Why did the Court reason that certain amendments in the Bill of Rights cast a "penumbra of privacy"?

The Supreme Court has ruled that the due process clause of the Fourteenth Amendment prevents state governments from infringing on the right to privacy.

Explanation:

The Fourteenth Amendment clause guaranteeing that no state shall "deprive any person of life, liberty, or property, without due process of law." The Supreme Court has interpreted the due process clause to provide for "selective incorporation" of amendments into the states, meaning that neither the states nor the federal government may abridge individual rights protected by the Constitution.

Although there's no enumerated "right to privacy" in the Bill of Rights, since the 1960s the Supreme Court has held that several amendments create a "penumbra" of privacy for individuals' private beliefs and conduct.