Nearly or every other part of your body feels pain (has pain receptors) yet the brain does not have pain receptors, so it does not feel pain.
No pain inside the brain
That is why you can see puzzling images of brain surgey on patients who are awake and only having local anaesthetic.
Also, why people can have nails and other things in their brain yet not feel any inside pain.
Why no brain pain?
Is it part of the brains design as a possible receptor/receiver of knowledge and information from the universe?
Or is it as simple as if the brain could sense its own pain then that may endanger your and its survival in moments of crisis?