Bitcoin is digital cash. It’s not physical money because it can’t be held in someone’s hand, but you can get that into your computer. You don’t need to trust us with your private key. We don’t know where it lives on the Internet (on our servers) and we don’t try to log into your bank account (our private keys are worthless because they only work for bitcoin payments). So, if you care about privacy, why would you store it with us? And even if you do want to store some of your bitcoin with us, there are other options (some better than ours), like https://localbitcoins.com .
Can i still use my wallet at coinbase?
Yes! Coinbase has compatible wallets, here