One attacks, the other receives this attack in order that, over time, moving and responding becomes second nature. One of the ground rules is that you don't hit back which in some circumstances means over-riding your automatic reaction with a learnt response. Being able to do this rests upon the skill of being 'centred'. Staying centred means keeping mentally at the place where you feel in control. When you move off centre you become unbalanced and are more likely to get caught up in an argument.
Assertion comes from centre, aggression is uncentred action.
So one of the aims of self defense is to help the aggressor find their sense of centre again, so they can discontinue their violent behaviour towards us right now and others in the future. The martial art of Aikido attracts students who want to learn self defense but not by the old way of the one who causes the most pain wins. As there is no glamour in this approach you don't hear much about Aikido but it has been taught in Australia for over twenty years and a look through the yellow pages under martial arts will find you a local practice hall.