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.