What is brain wallet?
Using a brain wallet means memorizing a passphrase and using it to derive keys and addresses, with no hard copy. This can be done securely, but it is very easy to choose an insecure passphrase and lose your bitcoin to hackers. Also, a long passphrase is hard to remember, band the coins are lost forever if you forget the passphrase. Finally, if you happen to die while using a bran wallet, the bitcoins die with you (paper wallets and other backups can be found and opened by family).
For those reasons, brain wallets are not recommended for regular storage.
Niche applications include holding on to coins in places they may be stolen or confiscated (prison, oppressive regimes (think 1984), very invasive border patrols, etcetera). If you use a brain wallet for this, be sure never to reveal its existence (better yet, avoid mentioning cryptocurrency at all), as you may be tortured and forced to reveal the pass-phrase.
These are good recommendation why brain wallet is not safe at all because of these risks, and if nothing happens we many times in our lives become sick and ill and we have many chances that we can forget a part of the passphrase and lose all the bitcoins on that wallet. Not mentioning the cryptocurrency in the public or to strangers is a good thing too to escape any surprises but we can't isolate ourselves because bitcoin is getting bigger and bigger and one day soon we will spend our coins on the right places.