There is some really, really good advice in here for those folks who might be struggling with identity and self-valuation in today's excessively connected culture. There are a couple of indelicate points, however, that I think bear addressing.
"Independent-mindedness" is a very, very leaky abstraction. It is certainly not a scalar quantity (as Paul seems to suggest), nor is it something one is born with. At best, it is a measurement of distance from the cultural mean, and culture is n-dimensional.
Culture is also contextual. Paul trades a little paint with this concept but fails to impact it fully. If you're trying to expand your understanding of the world (and consequently your ability to reason about it, which will help you think for yourself), one of the best things you can do is to travel / move / change jobs / insert contextual mix-up here.
He touches on some qualities adjacent to these concepts with stunningly good advice. Think for yourself. Be curious. Ask what's missing. Step back and see how people think. However, he notably avoids giving a name to one of the most important components of curiosity; that of humility. He talks around it quite a bit - but somehow misses calling it out explicitly. This feels like the kind of thing that someone of his considerable success might take a little for granted. Not that he doesn't have it himself, I cannot make an assessment as to that one way or the other.
This leads me to one of the things I found most dissonant about this piece; Paul absolutely nails it when he talks about having sovereignty over your thoughts. In the context of an article that's about "how to make it". Pressure to succeed financially or to gain social recognition is one of the most deleterious forces to a diverse culture of thought. Forgive me for getting a little political here, but IMHO it's the core reason that capitalism has an upper bound. Fiscal incentives are by their nature (and design) reductive.
From there, I have a couple of other, relatively minor, gripes. I'm as uncomfortable as many of the rest of you with how specific the prescriptions for "thinking for yourself" get. Furthermore, the idea that you have to insulate yourself against those who are different from you (even if you perceive that difference to be I'm weird and they're not) is fundamentally antithetical to expanding your worldview.
That being said, if you're struggling with feeling like the world is trying to put you in a box, the things Paul suggests here are helpful: Indulge your curiosity. Don't hang out with people who get down on you for being you. Humor and ingenuity are sibling concepts. Don't participate in intellectual fashion.
Most importantly, don't let people tell you how to think.