I am an about to graduate Computer Science student so probably this is a stupid question. If I have a class with a variable that is private and the class have getter and setter for that variable. Why don't make that variable public?

The only case I think you have to use getters and setters is if you need to do some operation besides the set or the get. Example:

void my_class::set_variable(int x){
   /* Some operation like updating a log */
   this->variable = x;
}

Thanks in advance!