An interesting and valid question. I suspect that the root of the problem is a commitment to non-violence at the core of her beliefs.
I'm going to suggest a good fantasy fiction book here that touches on this very subject. It's called Naked Empire by Terry Goodkind, and deals with a non-violent society that has been invaded by a very violent and oppressive one. It's actually one of a series by Mr. Goodkind referred to as "The Sword of Truth" series. You may have encountered a TV series that is based in the first couple of books in that series.
Anyway, the lead character questions this belief set and instills in this society the will to fight back by engaging in a series of discussions with people from this society in which he points out that the non-violent have given moral equivalence to all actions (that is, all actions are equally valid), and that they are claiming through inaction (failure to resist) that rape, murder, assault and theft are as equally valid reactions as preservation of life, charity, and so on. They have, in fact, equated preservation of life and murder as equally valid in the scale of human reaction.
I think that's the real crux of the issue. People have somehow come to believe that if they just are compassionate enough, non-judgemental enough or understanding enough, the bad guys will cease their rapine, pillaging, plundering and so on. Reality dictates otherwise. Reality says that these people, if they are not forcibly stopped, will continue on in their ways. What makes them stop is being forced to do so, either with direct force or threat of force. In the story you related, the threat of force (prosecution & jailing) is essentially a non-issue to the gang members. Police have indicated that they essentially have no leads and can't do anything to stop future assaults.
A moral and reasonable reaction is to bring the threat of force closer. Most people on this board agree that this is a reasonable reaction, and the method we generally prefer is firearms. Firearms remove the need for strength from the equation (I don't have to be strong enough to fight them off), equalize the disparate threat (it doesn't matter nearly so much if there are three or four of them attacking) and allow for graduated threat levels (I don't have to start off killing, I can threaten the use of deadly force).
This progression from non-violence to willingness to protect ourselves is not something that typically happens overnight or in the course of a single discussion. I would encourage you to read Naked Empire for its value in the arguments that are used, as well as any other resource you can find that discusses the topic of self-defense and the morality of such, and use the arguments you find to persuade this person. Also, don't give up because the person gets excited or angry. Back off from the topic and re-approach it another time. As they say, Rome wasn't built in a day.