The main reasons as to why non-violence and peace are ineffably linked together.

Nonviolence is the personal practice of being harmless to self and others under every condition. One possible outcome can be human unity. Nonviolence and Human Unity. Many nonviolence theorists see an even deeper rationale for nonviolence than the ones to which we have already referred. The essence of the practice of nonviolence is that it seeks to liquidate antagonisms but not the antagonists themselves (‘hate the sin but not the sinner’). This may be based on religious injunction or on a strong sense of the unity of all life: either way, this means that it is ethically wrong and existentially or spiritually self-defeating to treat another with less dignity than is warranted by a shared humanity or divine inheritance.

http://www.nonviolenceinternational.net/seasia/whatis/book.php