My kids are playing Animal Crossing New Horizons and Kapp'n won't take us on his boat.
I have verified and they have enough Nook Miles (over 15k).
We are not playing in English but if I translate freely he says something like: "I only take old sea wolf. You're too inexperienced. If you still want a ride go the airport first.".
Going the the airport we have the options for multi-player, going to Joe's island and something about buying a Nook ticket. We tried going to Joe's island. We waited a day in real life and tried again.
I'm not super familiar with the game. Searching online and it seems you just have to go up to him and pay the fee.
Best Answer
You have to take one trip with Dodo airlines before you can ride with Kapp'n. Early in the game, the Dodos inform you that Tom Nook gave them a free Nook Miles Tour ticket for you to use, sort of to use as a tutorial for using Dodo Airlines for these tours.
Kapp'n's tours are pretty identical to the Dodo Airline tours (with a wider variety of islands you can go to), so I suppose Kapp'n is making sure you know the rules of tours. He even makes a joke about this when landing at the island (saying something like "since you know the rules, I won't get into it").
Source: I also had this experience. My daughter's character had never uses their free Nook Miles ticket at the airport, and she was prevented from boarding Kapp'n's boat. After taking the airplane tour, she was able to use Kapp'n's service for 1000 miles.