1. When Coinbase gets hacked (not a matter of if, but when) their database could be published by the hacker and it would be free for everyone to see. It may even end up one some chain-analysis website like walletexplorer.com where people can easily search an address and see all the linked transactions.
2. When you end up sending bitcoin to a destination that breaks Coinbase's ToS and they shut down your account and seize your funds.
Thanks. So what is the best solution?