I maintain that our puny little brains aren't even close to capable of "reasoning out" the meaning of life, the universe, and everything.
The problem isn't our brain's inability to discover the meaning of the universe. The problem is too many people think there could be meaning to the universe. It is difficult for humans to turn off their deep desire to anthropomorphize everything around them. Just because a human can have intent does not mean that a rock, an apple, or a universe can. When you can tell me why my shirt wants to be blue (convincingly), I will concede it is possible for there to be meaning to the universe.
Asking "why does the universe exist" is no different than asking "what color is 1+6?" Just because a set of words makes up a syntactically correct question does not make it a valid question.
You nailed it there. The act of letting go the belief that people, things and the world have an "official purpose" is a difficult one. I've heard first hand numerous times from religious people when confronted with the idea, and the response is always disturbing. It goes something like this: "Then it doesn't matter what I do. I can break the rules of man and God. There is no reason to be moral or ethical." I can only guess that response is born of the fear and hopelessness felt in that brief moment when they imagine there is no purpose. The concept of purpose is purely human. We as sentient beings ascribe purpose to things (this bed is for sleeping because we built it that way); it's not an innate, natural property.