ok so I joined coinbase after the above comments and yes, while it doesnt give you your private key, so in theory you can transfer your bitcoin to your own wallet... i have uncovered another major hickup which i hope someone can explain.
to test, i added $50 ($48 after the fee) in bitcoin to my coinbase account. under the accounts there was an option to send payment, so I copied my binance wallet public key address as the receiving party. ok so far. just for $hits i entered $10... it found the binance wallet address ok, and i was ok to accept thier advertised transfer fee of 3.99%... HOWEVER, I it said there was a $30, yes THIRTY dollar miners fee to transfer $10.... ummmm.... what am i missing here?? thats not 3.99%, closer to 399%!!
The 3.99% is the conversion fee, I assume you bought with credit card. If you want to avoid the miner's fee, transfer your BTC from Coinbase to GDAX, and then send from GDAX to Binance.
Btw you should have used blockchain.info for your purpose as you wanted to have control of the private key.