I, like most fantasy writers, think a lot about magic. I mean, a lot. I love thinking about different magical systems and how they work, what their strengths and weaknesses are, and how they can be employed to make the coolest story possible. Dark magic, light magic, elemental magic, you name it. Magic cast with wands, or words, or motions. Magic that comes from special creatures or from the hearts or minds of humans. I love magic. What I don't love is when writers have weird hang-ups about magic.
The most notorious example of this is when a character says something along the lines of "It's not magic, it's bending/semblance/alchemy/etc." I assume this is an attempt by the writers to make their magic system seem more interesting and original, despite the fact that it's clearly magic with a different name. I wouldn't mind this, except that by coming out and stating "it's not magic", you're acknowledging that your setting has the concept of magic. So... what exactly is the distinction between "totally-not-magic" and, you know, regular old magic?
This distinction is occasionally addressed. Fullmetal Alchemist is very clear in pointing out that alchemy is governed by the rule of equivalent exchange, where you can't get something without giving up something in return, in a sort of mystical balancing of equations. Thus, we can conclude that "magic" would be getting whatever you want without a price. Philosopher's stones appear to do this, but of course are only created by using human lives in their initial creation; there is still an equivalent exchange. I'm also willing to give the "alchemy vs magic" thing a pass because it's based on the real world distinctions between alchemy—which was a mystical form of early chemistry—and magic—which generally involves dealing with spirits and supernatural forces.
But then we have stories where the "totally-not-magic" is blatantly supernatural or mystical, coming from spiritual connections or the souls of those who wield it. Bending in Avatar: the Last Airbender, for example, is when a human controls one of the four elements—fire, earth, air, and water—by doing a series of movements, or by controlling their breathing. There is a clear spiritual aspect to this, as the Dalai-Lama-esque avatar can wield all four elements in order to keep balance between the human nations and between the human and spiritual/natural world. Essentially, bending is elemental magic with somatic components. And that's fine! I love Avatar, and it has excellent world building overall, except for the line "it's not magic, it's waterbending." So, ok, bending isn't magic... then what is? We're never told. I think we might never hear the word "magic" after the first episode. So why bring it up?
More egregious, still, is in RWBY, were Weiss states that they have semblances (essentially, a magic special technique unique to each person) and dust (basically, magical material of different types) but not magic. Um... really? It's even more puzzling in Season 6, when we learn that the world was once crawling with magic wielders, but was reset so that no one who wasn't from that original time can use magic. Or, rather, "magic"; people can use their semblances to create illusions, and summon monsters, and have precognition. So why not call it magic? Why not say "semblances are just a portion of the magic that humans once had"? Or say "people used to be able to use magic without the aid of dust", similar to how humans in Harry Potter can only do magic properly with the aid of a wand?
If you want to fancy up your magic system by calling it something else, that's fine. If you feel a burning need to have someone say, "It's not magic, it's my own original character, Blagic!" then please take the time to explain why it isn't magic, and what exactly people in your world mean by the word "magic". Maybe magic is present in the natural world, and blagic (or whatever) is wielded by humans. Maybe magic can be done with nothing to fuel it, but blagic can only be done through certain rituals or by using special components. Or, why not just never, ever use the word "magic", since people in your setting just call it "blagic". Easy!
Another issue I have is when writers attempt to show that a character is ultra-rational by having them state, "I don't believe in magic!", even in settings where magic is a known and accepted force. In such a world, a disbelief in magic is like being a flat-earther or moon-landing denier in our world. An author could work with that, using this person's magic denial to characterize them as some sort of a tin-foil-hat kook, but I've never seen it played that way. "I don't believe in magic" is used as short-hand for "I'm a rational, scientific person", but does that really follow? As an aside, back in high school, there were some students in my theater class who made fun of me for being Christian, and who considered themselves to be far more rational than I. These same students, I kid you not, did not believe that blood types were real. Blood types! That isn't rational. That isn't scientific, and, in fact, requires the willful ignorance of settled science. It's the same for a magic denier in a setting where magic is a known, understood force. How does the character justify their frankly ridiculous lack of belief?
Both of these issues, I believe, stem from a misunderstanding of magic. The "totally-not-magic" systems always have specific limitations and rules, suggesting that these writers think of "magic" as boundless power. The "I don't believe in magic" stories contrast magic and science, as if magic cannot be studied or quantified. The thing is... that's not how magic works. And I don't mean how it works in fantasy; I mean, in the real world. I'm not saying that magic is real, I'm saying that real people throughout history have believed in magic. Sympathetic magic, hermeticism, witchcraft, and so on all have limits and rules, and can obviously be studied since, you know, people "practice magic". Specific actions are supposed to yield specific results. Even if these results are not supported by science, the idea behind magic is that there is a cause and effect relationship that humans can understand and control.
Thus, magic isn't any phenomena that can't be explained by science and that goes beyond the bounds or limits of the known world. We have a word for that: "miracle". Miracles don't have to follow any rules, and their cause can't be studied (though their results can!). Miracles are generally considered either inexplicable or divine in origin. Writers tend not to include miracles in their settings because it would be deus ex machina, as God is literally breaking into the story to fix things. While miracles are exciting in real life, they tend to majorly undercut the tension of a fictional story!
It might make sense to have a character say, "It's not a miracle, it's magic/bending/semblance/alchemy/etc," since, unlike miracles, the magic system has limits and rules. Even the most mystical magician could say, "I don't believe in miracles" and not sound like a flat-earther, since magic requires rigorous practice and study. Honestly, though, I would rather writers not bring this up at all. If your setting has magic in it, just let it have magic. No one who chose to watch or read fantasy is going to judge you for having magic in the setting, because that's what they signed up for. People like magic, and are more than willing to accept it in a fantasy, so instead of thinking about how much their blagic isn't magic, writers should be focusing on giving us the best magical system they possibly can, whatever it ends up being called.