Is it their regular wallet or their trading wallet? If it's the trading wallet, there may be an additional fee to withdraw.
I thought fees are lower for Bitcoin, am I missing something here?
There's a distinction between
service fees and Bitcoin fees. If you sign up for a company's service, like Blockchain's trading wallet, those companies can charge whatever fees they like. You don't get a say in the matter. But that's not the same as the fees you pay when you send Bitcoin transactions using your own wallet (one where you control the keys). When you use your own wallet, you can generally choose what fee you wish to include.
From
https://exchange-support.blockchain.com/hc/en-us/articles/360030874812-Deposit-Withdrawal-Fees-Crypto-:
*Please note that for all crypto withdrawals from the Exchange there is a small withdrawal fee charged by Blockchain.com which is taken from your total amount.