Why would anyone want to feel fake?
When would you want to feel fake?
Developing leadership skills means developing as a person, not just gaining facts, as in traditional classroom education. You change how everyone sees you and how you see everyone.
You change as a person, in other words.
While in limbo
While changing, you used to be person 1 and expect to become person 2. As person 1 you knew what brought you reward. You knew how to enjoy life.
As person 2, you expect to know what environments, beliefs, and behaviors will bring you reward so you expect to know how to enjoy life.
In between, you don't know how much of 1 you will retain or discard, nor do you know what new things 2 will require. So you're in limbo as a Frankenstein's monster of mixed environments, beliefs, and behaviors, some of which resonate with each other, others of which strike discord.
You feel fake.
What feeling fake means, in transition
But that fakeness is an essential part of meaningful personal change.
You don't feel fake when you learn how to bake a cake because it's too small a change to change you. Trying to change only a small amount doesn't make you feel fake.
After a few meaningful personal changes, you come to look forward to the feeling of fakeness as a sign you've taken on meaningful change and are progressing, having discarded parts of 1 and started experimenting with parts of 2.
It's why "fake it till you make it" is useful advice.