What does it mean when something is said to "contain ions"?
Your teacher is almost right but some terminology needs to be clarified.

Pure substances will almost always be electrically neutral (and the exceptions involve temporary local transfer of electrons from one substance to another as when you rub a rubber balloon on a wall surface). Beyond a certain level of charge separation you get enough electrical potential to cause sparks which allows the charges to equalise again. So persistent charge imbalance isn't easy to get. I think that is what your teacher means.

But if you look inside some pure substances, they do contain ions, just an equal number of each to avoid the bulk material having an overall charge. Common salt, for example, consists of ions (Na+ and Cl- in equal numbers). The substance is neutral, but the individual atoms making it up are all ions.

So your teacher is wrong if she meant that ions don't exist in nature but correct if she meant that bulk substances are electrically neutral.