So it looks Like Andi is in some sort of denial about her and Bandana's capabilities vis-a-vis leadership, based on a simple time-served, older=wiser personal bias thing.

Back in the days of wooden ships and iron men, teenaged boys from comfortable backgrounds who wanted a naval career would have a short time basic training ashore, then be posted to an active ship as Midshipmen. Whilst aboard, they had to carry out duties suitable to their rank of junior-most commissioned officer (which included commanding the enlisted men at simple tasks), as well as receive education in the arts of seamanship, and complete a certain amount of general education (after all, someday they would be real officers and be expected to have a certain level of knowledge about the world). The more comfortable your background, the more education you were expected to have, and the more expensive it was. It's quite probable that Andi's early days on board looked like: Get up before dawn and take astronomical readings, supervise the changing of the watch in a section of engine room, have breakfast, supervise some deckhands doing basic maintenance on the ballistas, have a lesson relating to her onboard job role, lunch, have another lesson relating to another part of her onboard job role, more supervising of deckhands doing basic tasks, have a general education lesson, dinner, stand watch under a more experienced officer, go off duty, bed.

If this is the case, Andi was probably working in the engine room from day one, and learning about them and how they worked and so on at the same time. She was probably babysitting between coming off evening watch and going to bed. On the one hand it doesn't say a lot about her ability to command (whether through respect of position, through respect of skill and talent, or through fear of physical retribution) that she can't keep an eight year-old reasonably calm, nor her problem-solving skills that she couldn't engage Bandana in making a game of helping her with her trig homework; on the other hand, she's babysitting for (from the name given and what we saw earlier) the second in command, who would probably be one of her teachers in shipboard matters, so she may have been apprehensive of exercising the full authority of her position as babysitter. In any case, it's highly unlikely that Mr & Mrs Secundus came aboard one day and were instantly given high positions in the command structure, so their family are clearly well-established on the Mechane by the time Andi joins, which leads to further implications that Bandana has been working up to command the Mechane for her whole life, meaning Andi is the counter-jumping interloper unjustly leapfrogging up the ladder in comparison. If Bandana only got an official position on the Mechane's crew when she was 12 or 14, she's not been a part of the official crew for as long as Andi.

In panels 5 and 6, we see Andi trying to cover for the precariousness of her situation. First she infers that she is the captain ("look who's in favour of the captain listening to other opinions"), then immediately accepts Bandana's assertion that she (Andi) is not the captain - she tries to throw doubt on Bandana's claim to the position rather than contradicting Bandana's claim. After that she simply abandons what little raggedy bits of reason and logic she was still clinging to and descends into outright personal attacks based on her historical inability to command, and her somewhat hypocritical sense that because she's older and has been officially on the crew longer, she automatically knows better.