you are your brain. You feel pain, therefore your brain feels pain. It doesn't have any pain receptors in the organ of the brain, but it interprets and feels signals from those receptors throughout your body.
Edit: it can also feel sadness, anger, hatred, depression, etc. All of which could be called being in pain. You wouldn't tell a depressed person on a ledge that they're not in pain
Christ you sound like an insufferable 10 year old with your 'facts don't care'. If you had actually read what you linked, you would have read the part where it specifies that the brain is what perceives pain even if it itself does not contain nociceptors. Claiming that the brain 'does not feel pain' is nothing more than semantic click bait.
As someone having lived years with unending pain and central sensitization, I find it hilarious someone telling me my brain 'does not feel pain because it literally can't'. Oh what I would give to be this healthy and naive again.
And you're an inflexible, unfeeling waste of cells. I hope for your sake you never have to deal with chronic health issues. Somehow, I don't think you'll be able to handle it.