Deposits are instant because the risk sits with you. Withdrawals pass through identity checks, fraud screening and bank processing, each of which adds time.
Financial businesses are required to confirm who their customers are. The process is called know your customer, or KYC, and typically involves an identity document and proof of address. It exists to prevent fraud and money laundering. See Wikipedia's article on know your customer.
Many services run this check at the first withdrawal instead of at sign-up, which is why the first payout is usually the slowest.
Outgoing payments are screened for patterns that suggest fraud: a new account withdrawing a large amount, a payout to a different name, activity inconsistent with the deposit. Flagged requests go to a person.
Where a promotional credit was used, the service checks that its conditions have been met before releasing funds. This is covered in turnover requirements explained.
Once approved, the payout travels over bank or card networks that have their own timetables. Transfers sent late on a Friday often arrive the following week.
Actual timings vary widely between operators. For the Taiwanese market there is this Traditional Chinese comparison of withdrawal speeds across several gaming operators (出金速度比較), which is a useful picture of the range you should expect.
A request for an additional payment before a withdrawal can be released. Legitimate services deduct fees from the balance. They do not ask you to send more.