You are really underestimating the complexity of the human brain. It is vastly more complex than the human immune system and the internet. 1 cubic millimeter was recently completely mapped and contains 57,000 cells and 150 million synapses. That is about 1 millionth of the total volume of the brain.
The immune system has 1.8 trillion cells which puts it between total brain cells (57 billion) and total synapses (150 trillion); and contains its own complex processes and interactions.
I’m not immediately convinced the brain is more complicated, based on raw numbers.
I don't believe anything in my statement amounted to a denial of the stuff you mentioned in your comment.