What is the cause that makes the Phaedra of Seneca a tradegy?
This is a good question. It is probably best to start with a definition of a tragedy from Aristotle's Poetics. Aristotle states:
"Tragedy is a representation of a serious, complete action which has magnitude, in embellished speech, with each of its elements [used] separately in the [various] parts [of the play] and [represented] by people acting and not by narration, accomplishing by means of pity and terror the catharsis of such emotions."
Based on this definition, we can see that Seneca's Phaedra falls into this definition. Phaedra is the wife of the great king Theseus. She, however, falls in love with Hippolytus, who is devoted to chastity and purity. Perhaps more importantly, Hippolytus is Phaedra's stepson.
When Phaedra approaches him repeatedly, Hippolytus rejects her and flees. Phaedra at this point tries to get the help of her nurse and they both fail to get Hippolytus. In this failure, Phaedra tells Theseus that Hippolytus tried to rape her. When Theseus hears this, he prays that the gods kill him. Hippolytus dies. Theseus mourns for his son.
Finally, the truth is revealed that Phaedra lied about Hippolytus. Phaedra kills herself and all are filled with sorrow.