"So can we land at this airport?"
"No, there is a crosswind of 19, the aircraft can only maintain 15kts."
However a reply of:
"No, there is a crosswind of 19, I have decided that for the time being my personal limit is 15"
would be fine. (As long as you'd thought up, in advance, your answer to the obvious next question: "so, if you knew you weren't going to be able to land, why did you take off then".)
(Having said which I did take off the other day knowing full well that I wasn't going to attempt the landing due to the crosswind. It was an IMC lesson, and I did tell the instructor before we started that I wasn't going to take off unless he did the landing, so no problem.)