Men stopped burning witches not because they stopped fearing them, but because they stopped believing in them.
Witches were still real, and still terrifying to Martin Luther and James I of England. But in the 17th century learned men in Europe began to use reason and to think scientifically, and they no longer believed in magic. By the mid-18th century almost no one took witchcraft seriously in the Western world outside the most ignorant peasants or the most benighted corners of Europe.
What happened? The Enlightenment spirit of inquiry, which rejected supernatural explanations of natural phenomena. The same men who disentangled natural science from Biblical scholarship also pried astronomy away from astrology. There was no place for the spiritual or the supernatural in their explanation of the universe.
As rationalistic and educated men came to hold power in the Church, they, too turned away from belief in witchcraft, regarding it as an ignorant superstition based in faulty understanding of God's power. The obsession with witchcraft also suffered because it was associated with medieval scholastic theologies which were falling from favor for other reasons. As early as 1610, no less authority than the Grand Inquisitor of Spain could write, "I have not found even indications from which to infer a single act of witchcraft has really occurred."
In the last witchcraft trials in the colony of Pennsylvania, in the first decade of the 18th century, juries would return no verdict but that so-and-so "has the reputation of a witch." The reality was out of the question.
By the late 19th century, the handful of believers still sounding a warning about witches, like Montague Summers, could only rail in futility against "The rationalist historian and the skeptic," who, when confronted with the evidence of witchcraft, respond with "a flat denial of all statements which did not fit, or could not by some means be squared with, their own narrow prejudice."
I know a woman many would call a witch. It's not the right word, but it conveys some of the right idea. She was a hereditary priestess in a very ancient craft, and she had powers. She was my lover for three years. I don't believe in magic or the supernatural. But I know she could do things. And she could see things.
And as a rational man, in a conflict between what I disbelieve and what I have seen, I have to put experience first. I don't expect you to believe this -- I insist that you not believe it. No one's word -- mine or any man's -- should convince you of things that are incredible. What happens to me is experience, but only to me. When I tell you about it, it is mere heresay.
I introduce her, because she had bitter thoughts about "the burning times," and the persecutions of her sisters by the early Church. But it occurred to me, too, that the early Church took them seriously, and treated them as a deadly serious threat. The social order in a community that looked to wise women with supernatural training for healing or cursing was incompatible with the patriarchal cell organization of the Church.
You can rail against the way the Church killed these people. But you can't deny it took them seriously. Witches were the ultimate gnostics. When our culture turned agnostic, it ceased to see them. We saw just odd, mumbling old women who thought they were casting spells to harm their neighbors, or young beauties who seemed to have a potent magical hold on the minds of young men.
So today you can see people who are upset by Harry Potter books as a lunatic fringe, but remember; the rest of us never resolved our feelings about witches, either. We just let them slip back underground.