That is disingenuous. An official conversation with a sitting President is automatically classified.
I’m sorry, you are wrong. If that were the case every single word uttered by a president to another in private would automatically be considered “classified” and that is not valid.
Conversations with the President are reviewed by any of a number of different agencies ie. DOJ, CIA, FBI, NSA etc. depending on the content/subject and then certain material is classified if adjudged to meet relevant criteria.