There were some things girls should not say in public. Take Charity Burbage, for example. Not only did she support intermarriage between wizards and Werewolves, she also urged wizards to understand Muggle research into wizards and magic. After all, everyone was curious, and curiosity was a force that drove the progress of the times.
She must have forgotten the saying that curiosity killed the cat.
If knowledge fell into the wrong hands, it became a tool for harming others.
Though there was no evidence, Pomona decided that Jack the Ripper had wanted to study women's bodies out of curiosity. Since he could never get his hands on one, he had no choice but to kill those women in the street and dissect them there.
It was an extremely humiliating method, much like parading naked through the streets. "Jack" possessed anatomical knowledge; that was something no one without medical training could fake. They had a grudge against some woman, then pretended to be Jack the Ripper, only to make a complete mess of the scene.
Knowledge could not be entrusted to the wrong people. If even medicine could be used to harm others, let alone magic. Charity's ideas had been naïve. She had angered someone she should not have, and brought about her own death.
Amelia Bones, on the other hand, had angered the Death Eaters of that time by speaking up for justice.
Jack the Ripper was already dead. Unless he had become a vampire, it should have been safe to discuss him now—unless some lunatic who worshipped him believed that "Jack" was not the sort of "coward" who lost all confidence at the sight of a woman, and decided to teach a lesson to the woman who dared look down on "Jack."
Men feared women looking down on them.