Link is...not a debater. At all. He shouldn't even be in this hall, but he wondered in by accident and then got distracted listening to all of the arguments happening.

This is a weird activity. But...Zelda would love it, he's sure.

And so he ends up vaguely hovering near Natalia when she makes her challenge - and makes an impulsive decision to respond.

"Caught a really big horse once."

...Although Link's might have a rather different view of what counts as boast-worthy than many others.