The sin of Adam and Eve, i.e., eating from the tree of knowledge, caused death to be the fate of all. The separation of body from soul is a punishment for the sin of Adam and Eve, who separated the fruit from the tree of knowledge.

If Adam and Eve had not sinned, they would have lived forever like the ministering angels:

It is known that death was decreed for Adam, who was the root of the world and the source of all humankind, and no one can escape it. For he died for his sin, and if not for his sin he would have lived forever like the ministering angels…

The sin involved the separation of the fruit from the tree of knowledge, and the resulting punishment is the separation of the body from the soul:

It is known from nature that when a root is deficient or damaged, the branches also sustain partial damage. The death of man means the separation of the soul from the body, and the punishment matched the sin of separating the fruit from the tree. This is the meaning of the statement of the Sages: “He clipped the saplings” (Tikunei Zohar 69); Adam is described as doing so because he sinned by separating, in action and in thought.

Further reading: For how we prepare for death, see A Concise Guide to Halakha, p. 77.

Because of the death decreed for Adam, even the perfectly righteous die:

Therefore, death is the way of the world for all, because they are the branches from that root, the descendants of Adam. It is unnecessary to state that this is the case concerning righteous people who sin, because even the perfectly righteous, who have never sinned, are included in the punishment of death, due to the decree against Adam, for we have encountered perfectly righteous individuals who never sinned, yet have died. (Rabbeinu Baĥya ibn Ĥalawa, Kad HaKemaĥ, Evel 1)