Enjoy your later courses on metric differential geometry, because you will be using r, s, and t as function names and c as a constant. And you'll also be using sin, tan, and cos, etc.
The way it works is that letters are taken for different things. So we like f, g, h as functions until we get more than 3, and then we do f1, f2, f3, etc. x, y, z are usually unknowns. And s, r, t, are things you call functions in domains that are more commonly physics based (I think. Someone should correct me if I'm wrong--but I know that they're taken). Training to communicate in this way is part of mathematical culture and makes it easy for mathematicians to interpret work at a glance. You can figure out much faster which kind of math you're reading, and which sorts of tools the author is more or less likely to use.
Similarly, we don't name the variables for our equations words, we name them letters; we've got a convention that a string like "egg" means "e * g * g," even if it would be cuter to solve for "egg" than "x."
So no, it is not incorrect to name your variables whatever you want from a technical perspective. From the perspective that math is a thing that humans read, however, it is best to listen to your teacher.