TITUS ANDRONICUS [...]Die, die, Lavinia, and thy shame with thee;And, with thy shame, thy father's sorrow die!SATURNINUS What hast thou done, unnatural and unkind? (5.3.5)
The audience is shocked when Titus kills his own daughter, an act that does indeed seem "unnatural and unkind." Why does he do it? According to Titus, Lavinia could never survive the "shame" of being raped. What's more, Titus can't stand looking at his daughter without feeling "sorrow," so it seems that he kills her for very selfish reasons.