The Fourteenth Doctor and Donna Noble had a short argument after losing the TARDIS on a spaceship before comforting each other. (TV: Wild Blue Yonder [+]Russell T Davies, Doctor Who 60th Anniversary Specials (BBC One and Disney+, 2023).)
The Ninth Doctor and Rose Tyler argued after rose saved her dad Pete Tyler's life and changing the timeline. They later forgave each other. (TV: Father's Day [+]Paul Cornell, Doctor Who series 1 (BBC One, 2005).)
The Twelfth Doctor and Clara Oswald argued after the Doctor left her to decided wether to kill the Moon or let it hatch in 2049. Clara later forgave the Doctor after realising his true intentions on a later adventure. (TV: Kill the Moon [+]Peter Harness, Doctor Who series 8 (BBC One, 2014).)