All he's trying to say is the world is flat is because when he looks at it, it is flat. When we look at it, it is round because we were taught it was round.
Then he tells us he didn't think the world was flat when he started to see it as flat. Though before that he said that he started to doubt that the world was round before he started to see it as flat. So his subconscious mind being unable to comprehend the evidence for a round world, while looking at a clearly flat one (though it's 25,000 miles around and your 6 feet off it), made it appear flat to his rational mind as well. Your subconscious is tricking your conscious into thinking the world is flat.