Think about it. The more you learned about your brain the more complex it would become. Also I’m not sure we have enough capacity to reflect on ourselves by processing everything. Think about the massive complexity of every connection. Could someone actually process that or are we limited by ourselves?
I don’t think brains get more complex because of additional information.
Also, what I’m not sure you mean with having “enough capacity to reflect ourselves by processing everything”? Do you mean analyzing another brain or analyzing your own brain? Do you mean processing every time a neuron fires, and which neurons get what kind of stimulus from it? Or do you mean looking at all molecules/atoms/fundamental particles and considering their state and following reaction?
I think we should be capable of understanding the concepts that make our brains work eventually. But I don’t think we have the capacity to monitor everything another brain is doing and understand/interpret it in real time, let alone our own brain. A computer might be able to at some point, when we understand more about neurology.