Section 1: First Rhetorical Question Summary

Get out the microscope, because we’re going through this poem line-by-line.

Why should I blame her that she filled my days
With misery, […]

The first question begins with "Why," and more specifically, "Why should I blame her?"
Right from the start, one thing is clear: the speaker does blame "her." Otherwise, he would not be wondering why he does, or should.
Sometimes it's appropriate to ignore the poet's biography when reading a poem, but in this case, Yeats's Irish readers would have known exactly who this "her" was: Maud Gonne.
Maud Gonne was an Irish actress and revolutionary. Yeats proposed to her repeatedly, but she rejected him just as many times. Politically, she was more of a radical and a nationalist than he was, which contributed to the failure of their love affair. For more on this dynamic, which is essential to the poem, we recommend you read "In a Nutshell."
The speaker blames Maud Gonne for filling his life with unhappiness. We can only assume that the reason for his "misery" is that she rejected him – again and again.
The tone at the beginning of the poem is one of anger and bitterness. Will this trend continue?

[...]or that she would of late
Have taught to ignorant men most violent ways,

Gripe #1: She didn't love him. Gripe #2 introduces politics into the mix: recently ("of late"), she encouraged simple, "ignorant" men to be violent.
From the reader's perspective, this is a much more serious accusation. So she didn't love the speaker: too darned bad. But inciting violence is serious business.
Yeats is talking about the role Maud Gonne played in encouraging violent, revolutionary activities in Ireland during the movement for independence.
Unlike the poor, simple souls she encouraged, Gonne was an educated, intelligent woman from a wealthy background. From Yeats's perspective, she should have known better. She doesn't have "ignorance" as an excuse for her radical beliefs.
Her support for political violence is a recent development, something that has happened "of late." She hasn't always been like this. "You've changed, baby!"
This poem was published in 1916, the same year as the violent Easter Rising in Ireland, in which Gonne and her husband played a role.

Or hurled the little streets upon the great,
Had they but courage equal to desire?

This is a funny image. Image a woman lifting up a small street and throwing it on top of another street.
That's not what's happening, though. It's a metaphor. The speaker accuses Maud Gonne of class warfare, trying to make poor, simple people, who live in the "little streets," rebel against the more powerful people who live on the "great" streets.
Imagine the residents of the Bronx invading the Upper East Side and you've got an image of the little streets against the great. Except in this case, the "great" streets are actually populated by colonizers, the British.
Yeats was a conservative dude, and he didn't have as much faith in the spirit and character of the commoners as Gonne did. The common folk have the "desire" to overthrow British rule, but they don't have the "courage" to carry out the deed. They are too impoverished and uneducated.
Yeats thinks that stirring up trouble among such people is reckless to the extreme.