I didn't say that neurologists don't treat the brain, I said that neurologists don't spend enough time actually treating the brain for my own tastes. Psychiatry is 100% brain.
And that's why I like psychiatry better than neurology. In neurology, you spend most of your time doing peripheral examinations, treating plumbing problems, etc. Stroke is a cardiovascular problem that affects the brain, MS is an immune problem that affects the brain, etc. Epilepsy and Parkinson's are primary brain problems, but that'll be a minority of what you see as a neurologist. Alzheimer's is a primary brain problem, but you can't really treat that effectively.
In psychiatry, we spend most of our time actually examining the nuances of what happens when something goes wrong in the brain. You get trained in how to track the progress of a mental status exam, when the rest of the doctors just circle the box that says "crazy" or "not crazy."
I think I might have oversimplified when I said that "the only specialties that actually treat brain problems are psychiatry and neurosurgery." I'll admit that neurologists do treat brain problems sometimes. But more commonly, their everyday practice involves examining PNS problems, peripheral manifestations of CNS problems, vascular/immunological/other problems that affect the brain, or untreatable illnesses. In psychiatry, you mostly see actual brain problems, and you mostly see actual treatable conditions. So psychiatrists treat more brain problems (it was a 2-part statement). That doesn't mean that psychiatry is superior... it's just the reason why I prefer it.