Ahimsa is Not hurting the Oneness, the wholeness of existence in one's thoughts, words and deeds. Once we understand this we can grasp what seems a dichotomy. Srikrishna exhorts Arjuna to fight and yet Srikrishna is extolled as Yogeshwara. This is because the duty of a Kshatriya is to protect the Oneness of existence. Kauravas had gone against Dharma and were thus behaving against Oneness. It was the duty of Arjuna to stop such Adharmis – the persons who hurt the Oneness of existence. Arjuna was hesitant to do that and hence Yogeshwara Srikrishna had to educate Arjuna through the Bhagavad Gita- the Yogashaastra.
Ahimsa is a personal value i.e. one person while dealing with another has to practice Ahimsa which means he should not hurt others. But Ahimsa is not a collective value to be practised. That is, suppose a group of terrorists attack our people we cannot say we practice 'Ahimsa' and we shall try to change the heart of the terrorist or Adharmis or enemies by practice of non-violence. Tolerating violent persons who hurt the society is itself violence. Thus a soldier who fights at the borders to protect his people, a revolutionaries like Bhagat Singh, Rani Ma Gaidinliu, U Tirot Sing, Veer Chilarai, Veer Lachit, Joymoti, Birsa Munda who fought for the freedom of their people from the atrocities of the British rule are definitely practitioners of Ahimsa.
Why should we not hurt others? It is because there is nothing called 'others' - the action ultimately hurts the perpetrator. Practice of Ahimsa implies not putting others to difficulties. Sometimes, even an apparently religious and 'good' action could hurt others like doing 'Japa' for too long and making everyone in the house wait for food, or deliberately chanting loudly when others in the house/room need rest or quietness. Practice of non-hurting is not just at physical level but also at mental level.
The one who really practices Ahimsa adds to the harmony of existence. As he never hurts, in his presence enmity ceases. Even if those who are hostile to each other if come near a person established in Ahimsa, they give up their traditional enmity.