It's not very easy to explain like you're five (it's like he says, to understand this requries more "up-front investment").

Maybe look in Kegan's wikipedia to have a better overview of what they mean by self-authoring mind (stage four in the big table)

https://en.wikipedia.org/wiki/Robert_Kegan#The_Evolving_Self

Do you want to go through life on a whim, at the mercy of your subconscious self, with no real insight into why you do the things you do, think the things you think, like the things you like? It's not psychopathic to want to tease out what you are, what you want, and once you do that, how to play the game of life such that you build your world to match what makes you happy?

This can be at a macro/life level, but it can also be at a much smaller scale. There was an example in the article on it, but to add another one that I think is similar: student submits an essay to the teacher, it's a good essay with better grammar, fact checking, etc than their friend's essay. Their friend's essay gets a higher score. Upon reflection, the friend's essay, while being lower quality, plays to the obvious preferences/biases the teacher has displayed throughout the term. For your next essay, you both do the high quality work, but you work in some aspects of what you now know the teacher wants to hear.

Is it manipulative or dishonest to do the latter? Some might think so. Other might think you are hacking the system to your advantage and hurting no one in the process.

Just read the description as well. "Self-authoring" seems to mean simply having an agenda that informs your behaviour. This could be interpreted as manipulative, but not psychopathic. Psychopathy requires a cluster of other traits such as deficient emotional responses and lack of empathy or control.