I think a lot of the women burned at the stake were accused of being witches because they were using herbs to heal people, and "doctors" couldn't stand to be outdone, and so accused them of witchcraft.

If that's true, it's not surprising. It'd be just another way the (Christian) patriarchal system relegated women to 'inferior' status. A woman tempted Adam, after all.
These men were and are terrified of women's power and, dare I say, superiority in many things. They reacted, and continue to react, with heavy-handed rules and laws designed to cement into place this religion-endorsed domination. Hopefully that's changed, or is changing. We'll see.

There were many male witches burned, hanged and drowned in Europe, witchcraft was considered an heretical religion and so was subject to the same punishments as any other heretic.
Wizard is a title and originally had nothing to do with magic (unless it was to study it from the outside for the purposes of fighting it)
Wyz simple means wise or learned and -ard one who does or practices and was seen as comparable with the biblical 3 magi, so were spared the fate of witches and those of more provocative terms such as sorcerer, thaumaturge, necromancer, alchemist.

Just as an aside male witches were always simply known as that until the 1960s when the TV show Bewitched decided that men could not be called witches because it was a "female" term and so replaced it with Warlock.
In Scotland Warlock was a legal term used in witch hunting and trials for one who aided and abated witches but was not one themselves.
Warlock simply and literally means Oath Breaker Old Norse varar and germen Schwur(sh'war) both from the Latin lurare meaning to swear a "solemn promise, vow" and Latin Luscus ‘One-Eyed’ or blind
Someone who breaks or is blind to their baptismal vows a blasphemy, therefore a warlock was a heretic.

To believe in religion, you have to train yourself to despise sceptical ideas, and accept high levels of cognitive dissonance, and when once you have done that, all other crack pot ideas become a lot easier. While the whole tone of thinking in the world you live in, is lowered.