The Hierophant
People seem to really hate The Hierophant. Most readers I know really struggled with this card at some point. It's especially tough for people who use the Tarot as a guide for introspection, or a sort of scaffold for a spiritual journey. The Hierophant often feels out of place -- like a strange intrusion of a wholly separate belief system into the Tarot. I think it has its place here, and I find that I'm a little more sympathetic to The Hierophant than many other readers.
Lets start by talking about why people are uncomfortable with this card. Just looking at it might give you a clue. It's a picture of the Pope. The card might not be called that, but it shows a person with a hat like the Pope's in a setting that sure looks a lot like the Vatican, holding up a hand gesture usually associated with the Papacy. He's sitting above the crossed keys that appear on the Vatican's seal.
In fact, up until the Waite-Smith deck, this card was called "The Pope," and the card now called The High Priestess was "The Papess." Waite and Smith made a choice to distance the card from the Papacy to some extent, but clearly they didn't want to totally separate it. The Christian imagery is a very intentional choice.
That's a key part of what makes people struggle with this card. I think it's fair to say that a majority of Tarot readers are not Christian, and are not particularly interested in Christianity. It's probably fair to assume that the majority of readers have an actively negative opinion of Christianity -- which, to be clear, is very reasonable! Most people interested in Tarot are interested in the occult writ large, and the imagery on this card feels like an unwelcome intrusion, a sudden appearance of stodgy, restrictive, formal religion in a system that was supposed to be removed from that world.
The general meaning of the card is also at odds with many occultist's worldviews. You'll usually hear it linked to things like "tradition," "conformity," and "societal institutions." Again, wasn't the journey into the occult supposed to remove us from all of these things?
For me, the clue to what this card is really about comes from the name change. Waite and Smith decided to keep the Christian imagery, but swap out the name for one that references the Eleusinian Mysteries of ancient Greece. These were secret initiation rites performed by cults of Persephone and Demeter. The High Priestess, formerly The Papess, was also renamed in reference to these rites.
"Hierophant" is a combination of Greek words that translates very literally as something like "One who shows holy things." In the context of the Eleusinian Mysteries, we can think of them as guides and interpreters. The High Priestess, their counterpart of equivalent rank, would assume the role of Demeter or Persephone. In a sense, she experiences these things directly. The Hierophant, in contrast is meant to guide the initiates to understanding.
I think Waite and Smith chose to alter the name but not the imagery to make a broader point -- both the modern Pope and the ancient Hierophant are examples of the archetype this card is meant to embody, one that is present in essentially every religion and belief system: a guide. The Hierophant is meant to embody the exoteric -- that which can be learned from others.
In a sense, this does mean tradition. If you go to most churches, most of what you hear will be exoteric teaching. But it's not exclusive to organized religion. Someone taught you about sigil magic. Someone taught you to read Tarot. Someone taught you which herbs to use in spells or what a spell was. All of that was exoteric. All of those people were The Hierophant.
When this card comes up in a reading, I think the key question is whether the querent is meant to be The Hierophant, or one of the two other people in the image. Are the cards saying that it's time to learn, or time to teach? You'll need to rely on context for that, but I find that it's usually pretty clear.
There's much more to say on this card, especially in contrast with The High Priestess, but I'll save that for the essay on that card.