Generally speaking, a player should not interrupt the DM to discuss how the rules work. What the DM says is final, and if the players do not agree with the way the DM is handling the rules, they must wait until the end of the session to resolve the disagreements.
So, with this player, you should be very clear and direct in telling them that, even if they are absolutely right, they should wait until the session ends to talk about mistakes or changes in the rules. Then, based on that discussion, you may agree to reconfigure certain events in the previous session, or you may agree to follow different rules in the future, or you may affirm that, instead, you will follow your understanding of the rules.
As a DM, you have a responsibility to make sure you understand the rules to the best of your ability. Players have specific class characteristics, actions they can perform during combat, spells they can cast, etc., etc. If you do not follow the rules as best you can (or do not make an explicit signal when you are not following the rules as written), it is more difficult for players to make informed decisions about how to play. their characters.
This is not necessarily limited to changes in rules or home-made material: an assistant will probably keep Identify in your spellbook to help identify the magical items you purchase, and if you are using the rules of the Variant Identification (DMG, page 136), where Identify the spell alone is not enough to completely reveal the properties of a Magic Object, they could be bothered if you do not inform them that you plan to use those rules in advance, since it was a decision of character creation that they took under false premises. Now, that is a relatively small example, and easy to handle in most tables ("Okay, I'll let you exchange that spell from your spell book with a free first-level Wizard spell") but the more substantial deviations could be more frustrating for the players, because if the rules are not well defined, the players will feel that they can not make significant decisions.
In relation to the above, the introduction of new mechanisms without taking into account how they interact with the world to which they have been introduced can have negative consequences.
An example that emerged in a recent campaign in which I participated was my DM's decision to add a new creature type to the game to represent the central villains of the campaign. I think the DM's intentions were to create a villain who was alien to Faerun's configuration, and it could be said that they were successful. But the problem then became that this new type of creature had no interaction with any of the skills or characteristics that any other character had:
- They were a NEWTYPE, so spells that say things like "affect Aberrations, Celestials, Fey, Demons, Undead and Elementals" would not affect them.
- His special abilities were from NEWTYPE, so, for example, a Paladin Aura that says "gain resistance to spell damage" would not affect his "Spell-like" abilities.
- This also meant that his features overlooked things like Anti-Magic Fields.
- Its damage type was VETETIPO, which means that no feature that gives Resistance to Damage (or Vulnerability) could interact with it, unless it reads something like "Resistance to ALL Damage", which is a very small subset of features
As a result, it was impossible, as players, to make meaningful decisions regarding how to prepare for fights with this type of creature. We could not revise the features of the class without just preparing them again, and we could not prepare spells to deal with these creatures because most of our spells did not work at all.
Eventually, we were able to convince the DM to incorporate the NEWTYPE creatures as an alleged addition to the "Aberrations, Celestials, etc." lists that have many spells, which allowed us to make tactical decisions when we approach these types of encounters.
Also in general, it has marked dramatically the frequency with which they appear in the meetings; We have spent more than a dozen sessions since the last time we fought against such a creature.
One thing I do as a DM is that I will spend a lot of time trying to examine the extreme case scenarios in D & D to better understand the interactions of the rules. Sometimes, if I see something strange, like a long-range goalkeeper who improves his chances of attack by blinding himself, I expressly decide that it is not necessary to follow the rules as they are written to improve the game.
But here is the trick: Even if I do not plan to follow the rules as they are written in a specific scenario, it is important that you understand what the rules are. areand why they were written that way, because that helps me better understand what problem I'm trying to solve and better justify my decision not to follow that rule.
Therefore, since these disagreements about the rules affect not only your relationship with this player, but your relationship with other players, it is important that you make sure you understand what the rules are and develop a good justification for not following those rules. rules as written. Planning meetings when you do not know what kind of mechanisms interact with them will end in frustration, even if players know they should not express that frustration in real time at the table.
D & D historically has its roots in the gameplay of Wargaming. Then, as a broad principle, a player who "plays to win" is not a strictly invalid method of playing. D & D, even the 5th edition, facilitates this type of metagame, "that's how we plan the strategy to win!" game, and many groups that do not play this way often do so by circumventing the mechanics of the game that they believe do not contribute to the style of play they desire.
However, the evidence suggests that this is not the kind of game you want to play. So, what is very important is that you sit down with your players and decide what kind of game you want to play. If all of you agree to want to play a Wargame-type game, or if you are all in agreement that you want to play a more social game, less focused on combat, then things will be fine. But if each one tries to play different games, then he will only have more problems.
Many problems at the table can be solved by discussing openly and honestly what does not work and what should change.
I've emphasized it so much by implication, but if you're willing to talk to your players about what frustrates you in the game and are willing to listen, I'm sure you'll find a solution that works for everyone. .