Interesting start. I guess this is a subversion of the usual fired trope. Normally the person being fired is an unforeseeable event that no one could have expected. Done purely out of cruelty and overlooking the person's importance to the organization. Mugi is a founding member of the guild and took no interest in the guild master position. This lead to an incompetent taking over that seemed to be running the guild into the ground until Ouell showed up. Mugi being fired is something he deserves and a consequence of his own choices.
Mugi is also emphasizing how talented Ouell is by saying "she was handpicked to be the guild master's right hand." We just established the guild master is a fat idiot. His opinion of someone is not a trustworthy indicator of someone's ability. It's more likely the guild master hired her because she's pretty than due to exceptional talent. That's just who the guild master is as a person.
Also the previous guild master couldn't have been that smart given that apparently the guild doesn't have any detailed personnel records. Otherwise the fat idiot would've known Mugi was a former high rank adventurer. Plus it shouldn't be so easy to force a founding member out of the guild so that's another point against the former guild master.