The most important thing that should be learned in school, and a crucial skill that will be carried throughout life, is the ability to learn.
This sounds simple but it includes things like accepting your failures/mistakes and accepting criticism as an opportunity to improve yourself.
I think the schools in the US fail terribly on this count; striving TOO MUCH to measure, in a standardized way, how/what students are learning.
Life is a continuous process of learning/maturing/growing and should be met with a vigor and excitement about the PROCESS.
The second "skill" that is crucial in life and not taught in school is how to interact with other people. Interpersonal skills are vital to succeed in any venture (except, perhaps as a violent criminal). This comes from diligent practice and, in my opinion, can be improved by taking a genuine interest in other people. Stop and "think about the other person" whenever you have an interaction with a clerk, a server, a stranger who is approaching the same door as you. Imagine they are having doubts and struggles much like yours. They feel insecure about many of the same things you do. Present a large smile, jump ahead of them in order to open the door and offer them entry before you. I do this ever day, in every encounter I have. It is never easy and requires much thought and concentration. But it makes living on earth much more pleasant.