@Kaelpie
Confidence and Arrogance refer to the same emotion, the only difference is whether or not you get results. Since Cosmo is going to get his shit shoved in for plot reasons it's arrogance here.
@Chrona
Word's definition aside, in most case it's just people's subjective view. One can saw it as confidence, but other might hate his attitude and called that arrogance.
Either way, being a bit arrogant isn't really a bad thing. Should Cosmo go into the match thinking "I leveled up, but I'm not sure if it's good enough"? Having defeatist attitude only made people giving up easily, so instead he could think "Yeah, I'm fcking strong, I'll win this!" and work his ass off toward that goal. You could say most fighters in this tournament are arrogant, since they always proclaim to be the strongest (until they got their butt kicked really hard).
@Chrona The difference between confidence and arrogance is that if you're confident, you believe you're the best while respecting the abilities of others.
Arrogance is believing you're the best because everyone else is trash. Which often leads to believing everything will be handed to you and berating others.
A good example of an arrogant character in this manga is Kiozan.