Meh. It's just a pattern. Follow the math here. It is generalized to *any* series where the next number is the sum of the previous two:
https://www.youtube.com/watch?v=dTWKKvlZB08
What this means is: pick any two positive integers, any. Use those numbers to start the series. Calculate the ratio of n / n-1, and it will converge to the golden ratio each time.
In other words, there's nothing special about Fibonacci numbers - it is just the pattern it makes as you calculate the ratio of the the nth number and the one before it. There are other series as well, sum of squares, etc. They all make patterns.
The mistake is thinking the patterns imply God.