Aristotle, who also stated in his POETICS that tragedy grew from dithyramb, and comedy from phallocentric spectacles.

Cambridge Anthropologists point to ritual

It is convenient to point to religious origins for Greek and medieval theatre; this can be incomplete (consider Rozik's argument that "theatre is a medium" while "ritual is a mode of action" (12).

Aristotle's descriptions of the sources of Greek comedy and tragedy.

Gerald Else (and others) on the origins simply out of the unique accomplishments of unique individuals (Thespis, Aeschylus, Sophocles, Shakespeare, etc.)

There is a religious element to Roman theatre too, but it is more civic and even commercial.