At the beginning of the play, Titus has just returned to Rome a conquering hero. He brings with him valuable captives. Tamara is not just any woman, she is Queen of the Goths. Accompanying her are her three sons and her lover.
As Roman military custom reqired, Titus, despite the heartfelt pleas of Tamara, sacrifices her eldest son. It isn't personal. It is the custom of the Roman army.
If Titus has a fatal flaw it would seem to be his sense of duty and honor above all else, including family when he kills his own son.
Once the cycle of revenge starts in the play it escalates to the final blow delivered by Titus to Tamara and Saturninus with his meat pies.
A hero or villain? I would have to vote for hero. Titus literally gave his life and the lives of his sons to serve Rome and was repaid with treachery. Did Lavinia deserve what was done to her by the sons of Tamara?
The sacrifice of Alarbus was not personal. It was part of warfare. Had the roles been reversed, it would have been the same thing. Titus or a son of Titus would have been sacrificed to whoever the Goths worshiped.
The rape and mutilation of Lavina was personal.
As a father, Titus had to exact his revenge.
I think that although Titus started this villianry between Tamora and himself, she pushed him to his limit. He truely is a Hero and only cared about Rome.