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Witchcraft has always been a secret art (which, ironically, is no secret). 
This is for a vast number of reasons. 
For one, if anyone finds out about your work, they have an advantage over you. If another witch knows, they can undo it. If a non-magical person knows, they can rat you out. 
For another point, it’s very clear in old world belief that talking about workings causes them to lose power. Revealing secrets and magical knowledge can actually spread them too thin and can cause them to wither. 
Some traditional witches don’t talk much because of fear that their power will be stripped for yapping. The spirits they work with don’t want them to go revealing all their hard won knowledge to just anyone. They will lash out if they feel that their knowledge is threatened. 
Folklore tells us of witches who disobeyed the Devil, revoked, or gave confessions. It tells of them being whipped, tormented by their circle mates, and stripped of their power. 

Then, of course, there is a different matter entirely, which is that some things cannot be put into words. Intense supernatural occurrences that can’t be confined within man’s mouth are ones that are also considered ‘secret’. The irony of it is that it’s only a secret because no one can really speak the truth of it. Just as many have grasped at how to describe the physical image of God or his angels, this is just the same. 

Yes, there is some knowledge that belongs to certain traditions that is barred simply because some aren’t initiated, but that can mean a few different things. It could mean that they wouldn’t understand it until they passed the tests required. It could also mean that the tradition is seeking to preserve itself in its knowledge, passing only to those who pass the initiatory rites (which, for some traditions, doesn’t mean spirit initiation at all). They don’t want their tools, their spirits, their concepts, or their methods being taken and inserted into another’s tradition (which is exactly what happened to Wicca). 

The thing is that traditions have every right to bar their knowledge and keep their secrets between initiates. It’s their knowledge. They’ll give it out at their own discretion. 
So many people have been lied to for so long. They’ve been told that they don’t have to do certain things to gain knowledge. They’ve been told that they have the right to access all knowledge at any given moment. When they find out otherwise, that there are underground circles of witches who harbor their own magical secrets, they get upset. 

The simple truth of it is that witchcraft has always been extremely secretive, living in the cracks and crevices of the world. As some wish to push it further into the light, others will recede into the dark. Those underground circles aren’t interested in showing the world what they do. They’re interested in surviving and thriving.