The arrogance isn't exactly unfounded.
Buckeye fans expect their recruiting classes to be shiny and coveted, every year, from the highest-rated recruit whose commitment ceremony was nationally televised all the way down to the high 4-star ranked at the bottom, whose Twitter commitment still went viral.
That's how it ends up going, so it's only arrogant in theory. Ohio State hasn't been a theoretical powerhouse in a very long time. We've been at squandered national championship cruising altitude with only mild turbulence for almost the entirety of the current century. That means natties are expected but also possible and realistic.