As far as the odds go, I really can’t develop it better than Givens has. If you move about in the world you have a reasonable chance of a violent encounter — greater than your chances of problems that other tools you can carry will solve, other than a phone (carry a damn phone).
For motivations, twofold. from the Catechism:
“Love toward oneself remains a fundamental principle of morality. Therefore it is legitimate to insist on respect for one's own right to life. Someone who defends his life is not guilty of murder even if he is forced to deal his aggressor a lethal blow:
If a man in self-defense uses more than necessary violence, it will be unlawful: whereas if he repels force with moderation, his defense will be lawful. . . . Nor is it necessary for salvation that a man omit the act of moderate self-defense to avoid killing the other man, since one is bound to take more care of one's own life than of another's.66
2265 Legitimate defense can be not only a right but a grave duty for one who is responsible for the lives of others. The defense of the common good requires that an unjust aggressor be rendered unable to cause harm. For this reason, those who legitimately hold authority also have the right to use arms to repel aggressors against the civil community entrusted to their responsibility.”
I find that entirely satisfactory. I am given authority over myself and my family, and I am thus given responsibility for their and my defense.
*** the cited passage is 66 St. Thomas Aquinas, STh II-II,64,7, corp. art — full text is interesting and germane at http://www.newadvent.org/summa/3064.htm — particularly article 7.