Killing yourself, in the Roman imagination, was infinitely more preferable than being killed. The privilege of suicide was often being given to members of the Roman elite who were being allowed to maintain some semblance of pride. The idea was that by doing this damage to themselves rather than having it done to them, they were preserving their will and ability to interact with the world in a meaningful way. They were not slave to circumstance, circumstance, or rather, their perception of circumstance, was slave to them. The significance of will to the Romans is unprecedented and tied in intimately to their notions of soul (i.e. animus). This notion was alive and well in the Republic, however, came into direct conflict with the power structures and nature of Imperial life. It is in the contrast between these romanticized Republican notions with the extreme centralization of power in the Empire is where you get the seemingly strange practice of Romans being forced to commit suicide

An example that I am particularly fond of and that displays the concept is the death of Astyanax in Seneca's Trojan Women. Astyanax, the son of Hektor, and the child-lord of Troy was caught by the Greeks who planned to throw him off a tower. Instead of being thrown of the tower, the young boy jumped and, to the Roman readers, this made all the difference. The Greeks, who had been caught up with the fervor of plunder, rape, and all the other activities of a sacked city, were moved to tears at the sight of the display.

Did this actually happen? Probably not. Even if so, the mythical events at Troy are so shrouded in mystery that we'll never know. However, it does show what thought patterns Roman writers projected onto the Greeks and that is still tremendously valuable. Seneca, a particularly influential adviser in Nero's court, (who would later be forced to kill himself) likely understood Astyanax's predicament all to well.

Another fantastic example is Cato the Younger (called Uticensis) who stood for the imploding Republic despite Caesar's insurmountable victories. Rather than accept Caesar's clemency (which would have meant accepting Caesar's will over his own and that of the dying Republic) he chose to end his own life. Although a bit grandiose, as he tore open the stitches that his family and friends tried to force upon his self-inflicted wound he proclaimed: "I must be the master of the course I am going to take!"

Another thing to add, Uticensis (his title after death) infers that despite his tactical defeat at Utica by Caesar, he was somehow victorious there. By the sheer power of will, he defeated Caesar because, through suicide, his will remained untouched and intact.

Adding to /u/bryminski comment on suicide as an option afforded to the elite in treason trials, the alternative was an ignoble execution followed by confiscation of your estate(s). By committing suicide when given the hint by the emperor, you could still pass on your estate to your children.