"Not just some petty quarrel...", Rex said fiercely.
Although he never really care about it, Rex knows that he can triumph over any student who is still learning in a university with the current power he has right now.
Even the alumni will likely lose against him, he's almost as strong as a Head Family right now.
Duncan Platchi who is the Head Family of the lowest ranking family in the 25 Golden Crest is just a tad stronger than Rex, his power is just incomparable to students anymore.
But his real goal is not that,
Rex didn't compare himself to students, it's not his end goal.
What he strives the most is to fight against Supernatural, and many other Supernatural are way stronger than him just like Anna from the Delarosa Family that he met before.
She toyed with Rex as if he's nothing, and he even got lucky by the Eternal Curse.