"the book said the plane could do it"?
The book says many things in absolute detail that the plane can do! Hence why there are takeoff graphs etc.
The problem with winds are there are too many variables so getting close to that limit can mean you exceed it.
When I landed the Seneca the wind was constant 40 kts. I had no real intention of landing but more an intention to touch and overshoot a sort of have a look!
It worked out ok and I landed but in the back of my mind was that I would not be able to make a landing from it.
As stated that was over twice the demonstrated on the aircraft.
Demonstrated is more of a guide that the test pilot reckons the average pilot who is a PPL and probably does not fly every day of the week can safely handle with a good margin built into that figure.
ie you may have a demonstrated of 15 kts and that maybe the figure given to you from ATC but in the landing that wind may jump to 20 kts! No one has control over that.
Pace