The Sanskrit term aparigraha, or ‘non-grasping,’ was one of Gandhi’s cardinal principles for residents of his ashram. This attitude of renouncing personal attachment to anything — a thing, another person, even an idea or opinion — is the key to self mastery, and also the spiritual key to freedom from coercion by others.  If you desire something for yourself (as opposed to wanting something for everyone, yourself included), that desire will control you, and others will be able to control you by threatening to withhold or take it from you.  If you renounce the desire, you unleash your own capacity to act in freedom, including the capacity to act nonviolently. This dynamic can be paraphrased as, “ask yourself what they are holding over you; renounce that, and you are free.”  As an example, when Daniel Ellsberg was deciding what to do with the Pentagon papers, he was at first paralyzed by what would happen to him if he made them public.  At some point it occurred to him to ask instead, “if I were willing to go to jail,” (that is, willing to renounce his personal freedom) “what could I do?”  He realized that he would then be free to release the papers, which he did. In the extreme, if you renounce attachment to your physical body, the threat of violence loses its power. To quote Albert Szent-Gyeorgyi, “[Gandhi] taught the world that there are higher things than force, higher even than life itself; he proved that force had lost its suggestive power.”
Renunciation also allows us to live simply on the material level, which takes the burden of scarcity from our fellow creatures and the earth.