Sexism aside, if we ignore the genders of Lyle and Ceres, they do have a point
While Lyle did say that Ceres had surpassed him in everything years ago, from what we actually see, the disowning of Lyle and promoting Ceres to heir was completely decided based on one duel
That is. . . . outrageous. Being a noble isn't even all about combat. It is incredibly irresponsible to decide the future of your House based on one event, one challenge.
Edit: Like, I suppose if she repeatedly shows up Lyle in every category, sure, I can see them promoting Ceres as heir.
But did they really need to oust Lyle from the family entirely? Absolutely not. Especially since at first Lyle was labeled as a prodigy, apparently. There's gotta be something else at play here.