The first decades of the 20th century were very tumultuous for Ireland, which was then still a colony of Britain. Irish intellectuals of all stripes, including both Yeats and Maud Gonne (the woman about whom this poem is written), believed that Ireland should be able to rule itself, but opinions differed about how to achieve this goal. As "No Second Troy" shows, Yeats did not believe that violent or aggressive tactics were ever appropriate, while Maud Gonne thought that episodes of British brutality demanded a more forceful response. The fact that Yeats was madly in love with this woman for much of his life throws another explosive element into the mix.
The speaker of the poem believes that a deeply flawed political order is better than a lack of order. He is willing to tolerate substantial injustice to avoid chaos.
The woman in the poem has "taught [...] most violent ways" through her example and her encouragement. She has not literally taught people to be violent.