A player at my table keeps belittling his closest and oldest friend and neither he nor I (DM) know what to do
Hello, it´s my first time posting on Reddit, so I´m sorry if my formatting is off. Also, English isn´t my first language, so there might be a few mistakes, I apologize for that too.
I (24 F) run a campaign with one of my best friends Lilo (25 F), her boyfriend Anton (28 M) and my boyfriend David (27 M). (All names are fake) David and Anton have been best friends for a long time but kinda grew apart a little. I have also only ever run campaigns for friends, so I´m not the most knowledgeable or seasoned DM.
We had a session 0 and have been playing this campaign for a year when Anton asked me if he could change his character. He got bored of his first one. I allowed it and he created one. He played his character as a know-it-all who took himself way too seriously, which David couldn´t stand. Since there were no rules broken I asked them to sort it out amongst themselves. They are good friends after all so it felt right at that time. I also don´t know everything that was said.
After that Anton decided he wanted to try to make a third character and play that one instead. I get the thrill of character creation so I don´t mind it. He created a new character and when it came to playing he yet again started playing a know-it-all. At the start of the session it was fine but as the session went on he started saying things like "I know how to do it in a better way than you! But I won´t tell you what it is because you´re the one doing it and i don´t get to do it!" (out of character) or just belittling him for his decisions and actions. This all was directed solely towards David, who was getting fed up. I tried to intervene and it stopped for a bit but I got told later that there were underhanded comments being said towards David that I didn´t catch.
I don´t know if that is something I should be handling, since I´m the DM, or if it´s something the two of them should sort out. I want everyone to feel welcome at the table but I also don´t want to put David through this again. He himself said that Anton ruined his fun playing DnD.
David and I talked about it afterwards and we don´t know why Anton does it only to David. I could be interpreting into this but it feels like he needs to put David down to feel better about himself? I don´t know, is there anything I can do in game to help or change the situation? They both play introverted and distrusting characters, so I really don´t know how I could fix this in game. I also don´t want to meddle in their friendship out of game.
Also, for context: Lilo and Anton are both in a relationship for the first time. That means that Lilo does not find anything bad about Anton´s behavior and basically worships and praises him constantly. In her eyes he can do no wrong. So talking to her wouldn´t help either otherwise I would´ve tried that already.
Another thing: I don´t play favorites. If I can´t decide who gets to do something like questioning the NPC I let the dice decide. The dice is visible to the players, so there´s no fudging the outcome.
I´m so sorry if it´s all over the place. I try to make it understandable while adding all the context I feel is necessary. I would really appreciate any help or advice on how to handle this.
TLDR: One of my players is belittling the other one and I don´t know how to correct it or if it´s my place to correct it
Edit: I told David about this post and he told me to seek advice for the both of us. He doesn´t know how to breach the subject AGAIN to Anton. Any advice for either of us would be greatly appreciated.