"quit classes" is a correct and usable phrase in written English.
You can use it when you are describing someone's decision to stop taking classes or lessons for a particular subject. For example, "I decided to quit classes for algebra after quickly realizing I was in over my head."
"But really, I can barely play a chord; I quit piano classes when I was nine because I wanted to play handball with the cool kids in class instead".
She quit taking classes at business school and left her job as an assistant coach for Stanford's women's soccer team.
The article said Haider had hoped to be a teacher but was forced to quit her classes when she became engaged.
Last Wednesday, in one of its boldest cross-border moves yet, a squad of uniformed, heavily armed Shabab fighters stormed into a Kenyan school in a remote town, rounding up all the children and telling them to quit their classes and join the jihad.
I fell in with a group of art students — painters, illustrators, sculptors — and even after I'd quit attending classes I'd still visit them, spending long afternoons on the cement floor of a cramped studio that two of them shared.
They all feel that the wrestling coach Mr. Connors's teaching of "real wrestling", or "wrassling", is too homoerotic and immediately quit the class to form their own backyard wrestling league called "the Wrestling Takedown Federation" (W.T.F ., much to the frustration of Mr. Connors.
Out of a group of 30 or so students, only 4 girls enrolled in the AP Computer Science class at her school, and the three other girls quickly quit the class because of the challenge and intimidation.
He still hasn't quit first-class cricket and is certainly planning to play on in T20.
But that's what Aquavit's Marcus Sammuelsson has done at Scandinavia House, where you can overhear people saying things like I quit Finnish class because it was interfering with my Icelandic while viewing an exhibition of avant-garde snowshoe art.
