My clients and I have been learning from each other
that the primary requirement for getting beyond adolescence
is telling the truth. This book deals with the whole problem
of telling the truth: the difficulty in telling the truth, how it
hurts one not to tell the truth, how we are all liars, and how
it works against our self-interest to lie. It is common for
people to ruin their lives and kill themselves through with-
holding. It is normal for people to stop growing and die from
an accumulation of mild stress disorders over time. Being
overweight, uptight, a heavy smoker, a heavy drinker, a non-
exerciser, or some combination thereof, are the direct result
of a more central ailment of the mind. These deaths come
from remaining enmeshed in the mind—trapped in lies. Es-
cape from the trap of lies is in learning, and improving
through constant practice (just like learning to play golf or
tennis), the ability to tell the truth.
We are all the walking wounded. Most of us are still
interested in clarity and the truth, but at the same time we
are interested in making a case for how our childhood was
worse than average and how we're better than everyone else.
The conventional way to suffer through life is to build a case
for ourselves. That is what you get taught to value in Catholie parochial school and law school as well as all other schools
(just not as efficiently as in those first two schools).
But at the same time we are all participants in a project
to find out what being alive is. And when we lie or hide or
avoid—essential tactics in case building—we don't discover
anything new about life and we don't help others to discover
anything new. Being interested in this common human proj-
ect of discovery is an important part of the great conversation
in which we humans have been engaged for several thousand
years. For my own good, I want to hang out with people
who want to find out what it would be like to live in such a
way as to leave no unspoken words, no unfinished business;
I want to be with people who are hungry for the truth, who
want to spend time learning and sharing what they have
learned rather than defending their images or reputations.
This book is for that group of people that is growing larger
every day—-those whose thirst for knowledge and willingness
to share overrides their defense against embarrassment. I am
writing for people who want to grow beyond the adoles-
cence that currently passes for adulthood, for the couples
who are fed up with acting and blaming, for individuals in-
terested in integrity or wholeness over moralism and fitting
into roles. This book is an antidote to that conventional suf-
fering. I hope it will piss you off and hurt you and inspire
you, and break your mind's hold on your spirit.

The word "radical," incidentally, originally referred to
the juice in fruits and vegetables, the moisture provided
through the root {radix in Latin). It later came to mean the
essence or substance of things. Radical does not mean "far
out," but, rather, "far in." Radical honesty would be the
core of truth, not just the outward trappings. Just as there is
"the letter of the law" and "the spirit of the law," so there is
literal truth and essential truth.

The lies that are deliberately told to others are IMO just a fraction of the total pile of lies.  IMO a large percentage of lies are lies we tell ourselves day by day and minute by minute when we are too weak to admit the truth to ourselves and instead would rather believe some pretty lies.  Those lies may feel a tad better over the short term, but long term, IMO they sap the strength and stability out of our lives and derail our road to success.  My personal opinion anyway.  I've known people who tried really hard to never deliberately tell a verbal lie, but the lies they told themselves were many. 

I like your thinking Eva! But the problem with "self-honesty" is: Everybody believes that they are honest with themselves, by definition!

First, I want to say that the following is my own interpretation and not having fully read the book, I can´t speak according to it.

Well, to go along with your example. The chance that this example would occur when you are radically honest and learned your child to be also, is small. The child would be open to you and you would have had a good conversation(s) with him/her. When there is radical honesty, the chance that your child would use marijuana is small. Why? Because when he/she has a problem, the child will tell you. Then you can together work it out, plus shared pain will already lessen the pain. So instead of struggling with the problems and covering it up by the use of drugs, the child can now with your support find a solution. I think that´s it with radical honesty, you can only do this when you are less attached to your experience, or you will become less attached because of the practise of radical honesty. When you are less attached, you are less ego-based and have more care for others(the child).
So in this example, the child and you haven´t been radical honest and suddenly at that moment, you want to be. That´s not realistic.

They don´t believe this if they are honest with themselves
You have to have mindfulness and wise reflection. The attitude to investigate the truth no matter what the results are. You have to use logic and identify false thoughts based on biased. Yes, this is a life long journey to wisdom. So your honesty will progress through your life. The decision to be (radical) honest is just the intention to put more attention to your experience and be truthful. The wisdom determents how honest you can be, but this is not under your control.