Holding cryptocurrency anywhere entails some degree of risk. But there are some additional risk factors that can make storing crypto on an exchange less safe than storing in a wallet. These additional risk factors include the risk of
a) an attacker gaining access to your individual exchange account, allowing them to steal your crypto
b) the exchange itself and/or it's wallets that communally hold customer assets getting hacked or compromised, resulting in the exchange being unable to process withdrawals.
c) situations where an exchange may lend out customer assets or borrow against customer assets, and suffers financial losses on those loans resulting in them being unable to pay out their customers (i.e. Blockfi, Voyager, Celsius)
d) situations where operators or insiders at an exchange elect to steal or abscond with customer assets.
e) an exchange shutting down for various reasons i.e. owners are no longer interested in running the exchange, or if they are pushed into shutting down for legal or regulatory reasons.
These risk factors are not present if users elect to store crypto in a self-custodial wallet instead, but choosing to store in a wallet also comes with it's own risk factors and responsibilities, including:
a) The risk of the user losing the ability to access their wallet where it's installed while losing or accidentally backups of the private keys or seed phrase. If this happens, the wallet will be inaccessible forever. There is no customer support to help users out of they lose these cryptographic credentials.
b) Improper or inadequate storage procedures that result in an attacker gaining access to the private keys or seed phrase, resulting in funds in the crypto wallet being stolen
c) Not having an appropriate inheritance plan in place.
Generally, it is safer to store cryptocurrency on a wallet of yours rather than on an exchange, but it really depends on the individual as well and whether or not they are in a capable position to secure their own self-custodial wallet(s) properly and if they care to take on this responsibility. If not, storing on an exchange may prove to be a better option for such individuals.
