Boxing originated in a place called Bellaux, which was a territory of Chaturanga on Sigrogana before the Empire gained control of the entire continent. Bellaux still exists and is not very far from the Arena (although it isn't represented on the map at the moment). Bellaux was always interested in people fighting for sport; the Arena is just one example of this, but fists were always the original weapon of choice. They would fight in arena-like cages, hence the name Boxer.
Insane FP costs makes them finish first and leave either themselves, their opponent or both dissatisfied.
They cannot combo with any other classes, since Schwarz Sturm only increases as they use Boxer skills, any kind of non-Boxer action, be it basic hit or even movement, will reset your Schwarz Sturm to 0.
Cobra Stance nullifies your damage. Matador Stance makes Regenshauer tickle, and you, vulnerable for a giant Retaliate comeback.
Enemies can try to survive with healing skills or spells until your FP runs out.
Hybrid enemies, who can both use Autohits and Basic Hits, can easily confuse the hell out of your Geist Schritt tactics.
Darkness resistance can halt a Boxer from stacking up Schwarz Sturm from spamming Asura Fist.
Evasion/Wraithguard + High Defense = guaranteed survivability, almost all of their damage is Physical, in nature.
Any kind of non-targetable spell or skill can outright ignore Geist Schritt.