I completely agree with grimbletart. I find it interesting that we seem to be equating self-defence with violence.
First, because as Lweji says, self-defence is not just violence, it is a whole group of things to protect yourself.
Second, because self-defence has for centuries been considered a legitimate form of violence, both at the country and individual level. The law does not expect you to just accept violence, whether you are a person or a country, you are allowed to defend yourself. Survival is a basic natural right.
Except -- this doesn't seem to apply to women so much, or women have been socialised in ways so as to suppress our natural self-defence instincts. We must be nice, we don't want to hurt people, even if they are being dodgy and trying to rape us.
So I'm not sure I would specifically teach martial arts, but I would definitely teach women and girls that they should listen to their instincts, that they have a right to protect themselves, and a range of tools to help them do so.
I understand people's concerns about victim blaming but that is happening anyway. And I think it's more likely we will be able to change social attitudes about that than we will be able to eliminate violence.