I do not plan on paying for an item since the cashier made a mistake adding it.
Why would you not pay for the item?
If she hadn't insisted that it wasn't rung up wrong, I would have let it go.
I understand that. If the cashier makes a mistake, it is good for the customer to point it out to them.
She said it wasn't and kept trying to talk me into paying for it.
Well if you know for a fact that they made a mistake than you are right for not paying. If it becomes a bigger issue at this point you are better off just leaving the store or putting that item back.