No, "both sidesing" is not at all how philosophers or mathematicians train to establish the truth: they learn to identify overt and hidden assumptions and question the validity of this assumptions.
This might happen when you imagine you truly hold some other position, but it is clear from the structure you describe (mostly unstructured talking to an opponent) that this is incidental learning and not the focus of the exercise.
What you describe is plainly a exercise in rhetoric, the central conceit that one can simply switch positions after a fixed period of debate is clear enough evidence that truth seeking is not the goal.