Having read up to date with the light novels I now understand the dirty looks over the Katrua game so much better, she's basically teaching these tiny orphans stuff nobles don't learn until a year or 2 before high school.
A high school that is a highly competitive environment with nation wide...
and they fight and they fight and they fight, and they fight and they fight, and they fight, and they fight, and they fight.... and they fight and they fight and they fight!
and all one sided of course