I've always been under the impression that Parseltongue is an inborn ability, not a teachable language, and it appears that J.K. Rowling holds the same opinion.
I was just reading a transcript of her pivotal Q&A at Carnegie Hall (the one where she revealed that Dumbledore was gay), and it turns out
she addressed exactly this question: Q:
Since Ron is able to speak Parseltongue in the last book, does that mean that Parseltongue is a language that most witches and wizards can learn or must a person be born with some ability to speak Parseltongue?
JKR: I don't see it really as a language you can learn.
So few people speak it that who would teach you?
This is a weird ability passed down through the Slytherin blood line.
However Ron was with Harry when he said one word in Parseltongue, which I do not know
so I cannot duplicate for you, but
he heard him say "Open," and he was able to reproduce the sound.
So it was one word.
Whether he could learn to speak to snakes properly is a separate issue.
I don't think he could.
But he knew enough, he was smart enough, to duplicate one necessary sound.
She phrased it as an opinion rather than definite fact, but it's still hard to argue with.
Plus, there's the fact that non-Parseltongues can't hear snakes speak, which makes it physically impossible for them to hold conversations with a snake.
That means that as a language, Parseltongue would be limited to novelty secret-language status — hardly a useful thing to spend your time on.
scifi.stackexchange.com/users/348/Martha
Parselmouths are rare There are very few confirmed Parselmouths during the events of the Harry Potter books.
Harry himself, Voldemort, the Gaunts (Voldemort's relatives)
- I think Dumbledore was said to be able to speak Parseltongue as well, but I may be making that up.
That's a very, very small number.
Dumbledore had enough problems finding Defense Against the Dark Arts teachers to fill the position, I imagine it would have been even worse trying to find a Parselmouth to fill a teaching position as well; there are considerably more witches and wizards who know about (fighting) the Dark Arts than are able to speak Parseltongue.
Add to that the fact that it was seen as a talent only possessed by those who had an affinity for dark magic and people may not even be willing to publicly admit to it.
It's not a particularly valuable skill
Ignoring Harry's very unique situation as The Boy Who Lived and his relationship to Voldemort, there's really no need to be able to speak Parseltongue.
Your average witch and wizard could go their entire lifetime without being held back by not being able to talk to snakes.
Hogwarts student timetables were full enough already Between classes, homework and revising for exams (when applicable) students had more than enough to occupy their time at school.
I'm not sure they'd have enough time to dedicate to an additional lesson to learn a language.
scifi.stackexchange.com/users/5833/Anthony Grist
I was under the impression that being able to speak Parseltongue was considered a sign of bad character; Voldemort was a Parseltongue for one, and as the Snake is both part of his motif and also his sidekick (In Nagini), snakes were considered bad news..
I think that during The Chamber of Secrets , certain Hogwarts students take this out of proportion (as Children are wont to do) and as such the stigmatism attached to Parseltongues is perhaps not as aggressively pursued in the rest of the Poterverse as it is in the highly charged microcosm of Hogwarts.
In short, I'm not sure it'd be encouraged because although perhaps useful, it could be frowned upon: similar in our universe to teaching children how to hypnotize other kids or picks locks...
Alohomora, however!
scifi.stackexchange.com/users/16267/John Smith Optional
The language of snakes is Parseltongue .
As to why it isn't taught, there may be some contradictions in descriptions of Parseltongue; the Harry Potter wikia describes it as a very uncommon skill, and is typically hereditary which suggests it might not be so much that it isn't taught as that it can't be taught; you're either born a Parselmouth or you're not.
But the Wikipedia entry describes it as a skill acquired through learning or via a method of xenoglossia Being a Parselmouth is described as being an attribute of a Dark Wizard, which probably means prejudice in the normal wizarding community contributes to
it not being taught as a matter of course at Hogwarts.
scifi.stackexchange.com/users/186/PhilPursglove
It is possible that Parseltongue is not taught because it is associated with Salazar Slytherin and Voldemort.
And in the minds of the wizarding community, it is associated with evil.
Prejudice is probably the reason why Parseltongue is not taught.
scifi.stackexchange.com/users/41199/Elizabeth Moore
There is the possibility that Parseltongue cannot be learned.
It is not a language, and it is magical in nature.
When Harry speaks it (or listens to a serpent speaking it) he doesn't even realize he's not speaking English.
This strongly hints that Parseltongue is actually closer to glossolalia (which is by definition miraculous / supernatural)
than to real language skills.
You are not born with knowing your mother language, you learn it.
however, you are born with Parseltongue.
When Ron imitated Parseltongue it was just how parrots imitate human speech.
Parrots cannot learn a human language, they just record and replay a few phrases as they would do it with any generic sound effect.
Another hint to it not being a real language is that WTF snakes are sentient ????
This means Parseltongue is either completely impossible, or extremely difficult to learn.
scifi.stackexchange.com/users/4004/vsz
Even though it is not a human  language  per se and that one had to be  gifted  to be able to speak to snakes, why didn't Parselmouths teach others Parseltongue, at least in Slytherin house at Hogwarts?  Ron spoke Parseltongue from watching Harry speaking it in  Chamber of Secrets . Hence Parselmouths aren't the  only  ones who can speak Parseltongue and be understood.
Why is Parseltongue not taught?
scifi.stackexchange.com
<harry-potter>
scifi.stackexchange.com/questions/43059
scifi.stackexchange.com/users/None/
Teaching Parseltongue may not be considered enough of a valuable skill to dedicate school time to this subject. Ignoring Harry's unique situation as The Boy Who Lived and his relationship to Voldemort, there's really no  need  to be able to speak Parseltongue. It may also be a strange ability passed down through the  Slytherin blood line. Prejudice may also be a factor in the decision not to teach it as well as the difficulty in finding a Dark Arts  teacher able to teach it. Parseltongue is a language that cannot be taught since it is passed down through the Slytherin blood line. 
Parseltongue is a language that cannot be taught. It is passed down through the Slytherin blood line. 