Easy. Cause no one else here could be your Captain. On the open seas the Captain has to be the strongest aboard a vessel in order to protect those who agreed to support him as a crew.
More bravado. But perhaps she was being overly critical--the whisky helped there--because most if not all captains had their own fair share of confidence. It was a necessary part of being a Pirate Captain, the show. The dare. The absolute "only a crazy bugger would do this so I'm going to do it" attitude that gave people places in history. She knew she was strong, and her Haki told her that he had his own strengths, but was that just an illusion caused by his Haki or if, like many Pirate Captains, he'd eaten a Devil's Fruit?
"Prove it," she said, all business as she stood looking at him, but still speaking softly. This didn't need to be a big display, especially if she ended up joining his crew. "There's a little space out back where they used to have an area for outdoor games, it's just sand now. Spar with me, show me that you've got the iron in you to lead a crew to greatness, and I'll be your First Mate. I've got to warn you, though, once you have my loyalty, I keep it until you break faith. So I hope for your sake you intend to follow the Code."