A variablealwaysstands for something! When a teacher says that a variablecanstand for anything, he/she is saying that the particular value can be anything. It does not mean that you can replace that variable withanythingand get a true statement.

As for your a= -a, "a"cannot'stand for' -a because -a is another variable, not a possible value of a variable. In fact, if a is a variable with the property that a= -a, then (assuming a is a number or, more generally, an object in some algebraic system with additive inverses [so that "-a" makes sense]) we can add a to both sides to get 2a= 0 so that a= 0.Thatis the value a represents.