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In Harry Potter and the Half Blood Prince - Chapter 9, Slughorn says (emphasis mine):

"I've prepared a few potions for you to have a look at, just out of interest, you know. These are the kind of thing you ought to be able to make after completing your N.E.W.T.s."

One of the potions in question is Amortentia - the most powerful love potion in the world. Why exactly would anyone in the Wizarding World ought to have to be able to make it?

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    I'll never need to know how to titrate NaOH with HCl of unknown concentration to find the concentration of the acid in my profession or in my personal life, but I still know it. Sometimes you learn things in school you won't need in the future. I don't see why there would be a practical application for everything in Hogwarts either. When are they going to need to transfigure a needle into a match or a hamster into a teacup? There's also the argument that knowing how to make it/what it looks like could help you avoid it. – Wraith Leader Sep 26 '17 at 14:22
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    Ah yes, the dreaded titration. I suppose you are right and there is no correct answer for this one.. – sudhanva Sep 26 '17 at 14:28
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    I mean, I may have jumped the gun, the way you ask the question may leave it open to a good answer. "Why would anyone need to be able to make it?" asks for the use case, not why everyone in the school would need to be able to make it. – Wraith Leader Sep 26 '17 at 14:34
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    To be fair, it doesn't say that you need to learn to make that particular potion for your NEWTS, but it does give a relative difficulty of creating the potion. It is certainly possible that creating such a potion would be on the standard test, but it is not a given. – Jeff Sep 26 '17 at 15:19
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    I think you're misunderstanding Slughorn. He's not saying "You ought to be able to make this potion because it will help you in your life." He's just saying "By the time you're done your NEWTs you ought to be this good at making potions, because otherwise you'll probably have failed your NEWTs anyway. – MissMonicaE Sep 26 '17 at 15:43
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It is no doubt a complicated (i.e. advanced) potion to make. That is why it would be required for a N.E.W.T. exam. The difficulty in making it demonstrates a level competency in potion making.

As to the ethics of teaching students something like Amortentia, almost everything about the magic world can be used maliciously if they want to. They spend a lot of time transfiguring objects, and it has been shown you can transfigure humans as well. So a gifted student could do that to Muggles (or whomever) and it would be just as unethical as doping someone with a Love Potion.

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    Possibly it is a good thing to know how to make Love Potion in order to create an antidote. – TimSparrow Sep 26 '17 at 14:41
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    Well, there definitely are going to be kids who don't really think it's malicious. "He/she looks so cute but would never date me. But what if I use this crafty potion that our prof was cool enough to teach us?" We are talking about a bunch of teenagers here. – sudhanva Sep 26 '17 at 15:15
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    It definitely seems like a dubious concept at best. In the real world, even dangerous drugs like rohypnol have innocent applications; I'm not sure how a love potion could be used in any other way. – PlutoThePlanet Sep 26 '17 at 16:31
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    As Lukyanenko pithily pointed out in NightWatch series, who needs Fireballs when you can cast "peel potato" spell on opponents to grate their skin off, and then finish them off with "Iron clothes" spell on their body. Magic in inherently deadly if used creatively. – DVK-on-Ahch-To Sep 26 '17 at 18:06
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    @PlutoThePlanet maybe a love potion is the only way to get certain magical creatures to breed in captivity. A perfectly valid reason to both make and teach it in school. – Jack B Nimble Sep 26 '17 at 18:31
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Slughorn had a specific motive - he wants to find those naturally talented students so he could form more connections with those wizards and witches most likely to become powerful in the future. To do so he not only needed to present difficult tasks, but also suitable motivation. The boring but complex potions will hardly generate the interest that a love potion would generate, and it might be enough to bring the cream of the crop to the top.

Even if that weren't the case, education often teaches hard concepts one may never use in order to demonstrate principles, and strengthen the foundation of one's understanding of a topic. In the same way that understanding a complex and difficult recipe can help a chef prepare simpler recipes when called on, understanding a difficult and complex potion will make understanding easier potions - and creating them from scratch - possible. You may never use calculus as an adult, but you know that a pool with a sloping bottom will fill more slowly as it nears the top despite the same rate of water input, and you'll know why.

Further, magical practitioners also need some experience with the more nefarious potions so they can identify them when needed, or avoid them if someone is attacking them in a hidden manner. This could be taught in Defense Against the Dark Arts, but it properly belongs in potions and teaches several things there.

I suspect this was also simply Slughorn's teaching method. While Snape focused on the foundational ingredients and preparation of potions, Slughorn discussed the high level concepts and results one could obtain.

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    I was going to say "But then Slughorn will fill his parties with would-be date-rapists!" ... and then I realized that would probably help him get in with the elite powerbrokers of the Wizarding World. :( – MissMonicaE Sep 26 '17 at 20:27
  • Wouldn't they have a set curriculum? How would it vary from teacher to teacher? – sudhanva Sep 28 '17 at 3:19
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    @sudhanva the potion master gets to set the curriculum. Snape set his own curriculum, slughorn set his. Recall when Crouch (in the form of mad eye moody) started teaching dark arts he specifically stated he’d be teaching it differently - the professors are given wide latitude to teach according to their expertise, and are specifically chosen because it’s expected they will develop a good curriculum. – Adam Davis Sep 28 '17 at 3:58
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    @MissMonicaE They get away with it because going to Azkaban would ruin their Quidditch career. – Studoku Sep 28 '17 at 10:06
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Taking your quote here:

"I've prepared a few potions for you to have a look at, just out of interest, you know. These are the kind of thing you ought to be able to make after completing your N.E.W.T.s."

Note that he says that they are the "kind of" things, not the "things." This indicates to me that once you have passed the NEWT and are acknowledged as having magical mastery at that level, you should have the ability to follow the necessary directions and successfully perform the necessary and intricate steps to successfully make the potion.

I used to teach organic chemistry. I don't expect anybody to remember years later how to make aspirin. But they should have learned well enough to remember how to do a filtration step, or how to do distillations, or any number of other chemical procedures.

Chefs similarly were classically tested on the quality of their hollandaise. They may never need to make it, but they would be expected to have the skill necessary to be able to do so.

  • I was going to make this point, but you expressed it so much better than I would've. – Doug R. Sep 27 '17 at 1:57
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I know plenty of chemistry students who have learned how to make some pretty serious illegal drugs in university labs. Obviously this is just for displaying the technique which is what I would imagine this was. The students are never actually meant to do this again but it sounds cool and gets their interest.

Certainly these things are the only things I have heard them excited to tell lay people about so it seems to work.

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