Maybe I'm blind, but I don't see anything about Monica being forced to pretend she was worse than her brother, do you?
When Monica was young, many labeled her a child prodigy. She learned to read, write, and calculate with great speed, quickly catching up with the academic accomplishments of her brother, who was two years her elder.
Although such exaggerated excitement about her talents settled down as she reached her tenth year, she was nevertheless recognized throughout courtly society as a very bright girl. As her father’s status as a minister among the Nobles of the Robe afforded her free access to the books in the palace library, she read often and learned a great deal.
Her ability to quickly absorb material proved useful in other fields as well. Her father allowed her to begin learning self-defensive martial arts from her brother’s tutor, a knight, and she swiftly progressed in her training.
As Hasenvalia permitted women to participate in military service, Monica enlisted in the royal army at the age of fourteen with the aim of receiving a knighthood, partly to challenge her own abilities. The royal army was in the process of expanding the scope of its structure at the time, and so it was actively seeking out well-educated individuals of solid lineage to serve as officers.
Yet the manga adaptation makes a whole point about it...
Honestly, I'm just not sure what making Monica's relationship with her brother worse than the LN version accomplishes.