How can I move bitcoin from one exchange to another without mining fees?

At the time coinbase opened one could type in the bitcoin address and public and private keys from paper into their wallet and voila the coins were available for trading.

Let's take a look at the implications of sharing private keys for value transfer. Sharing a private key with another party introduces ambiguity of ownership. Both of you can now spend the coins. Even, while the exchange now has spending access, so do you still. Therefore, the exchange must sweep the key in order to take possession of the funds and credit you a balance on the exchange for trading. This means that either way your funds need to be spent to be deposited.
Next, the shared key raises the question who the receiver is supposed to be if the address gets paid again later. What would you like the outcome to be? Would you expect the exchange to keep track of this custom address, sweep it and credit you? Expecting the exchange to keep track of thousands of custom addresses that don't fit into its regular key management likely introduces major scalability and security issues. E.g. they can't be tracked by a standard HD wallet approach, nor can keys be added to an HSM easily. Or would you rather like the exchange to only use the key once and then forget it? Since the key is no longer secret and only known by you, you would still need to consider it compromised.

So, since a transaction is already necessary, it's simpler for all parties if the user deposits funds to the exchange. It simplifies tracking, makes custody unambiguous, doesn't cause the address tracking scalability concerns, and allows the user to determine a fee rate that properly signals their time-preference.

However, it appears that nowadays one is asked to transfer bitcoins when moving to another exchange and that option has evaporated.

While we are still in the early adoption stages, some companies have started integrating tools to transfer balances by other means than on-chain transactions. They might use Lightning Network, or derivatives like Liquid Bitcoin, XRP IOUs, or ERC20 tokens. While that may reduce operational cost, each of these has their own trade-offs.

It makes no sense at all that I should pay mining fees when I already own the coins. I certainly believe the fact that there always seems to be a mining fee involved even though one may not spend the coins is one reason that bitcoin is still useless in day to day economy. I can give someone 100$ in cash, but I cannot do the same with bitcoin because I loose a fraction due to the middleman taking a cut. I can’t believe that there is no way to avoid the mining fees when moving from one exchange to another. I am happy for any useful advice.

When you give someone $100 in cash, you have to be physically present, need to wait for them to count and verify the bills as well as ring you up a receipt. If you value your time, in person payments have an actual cost. It's just that the cost is paid from a second resource, your time, instead of the medium of exchange. It's not clear to me how your example supports the notion that payments should be free.

My advice would be to take a look around at how the best-practices in the industry have evolved and to adjust to the current modus operandi. Sharing private keys seems like a terrible way of conducting payments.

As far as I know this is not possible with any centralized exchange anymore, but it is not relevant because you would still pay a fee when you sell the bitcoin. I you don't want to sell, it makes no sense to move the bitcoin to an exchange anyway.

Depositing 100$ in cash to an exchange is probably more expensive than the $ 0.10 fee for Bitcoin. You would have to travel with your 100$ in cash to an exchange or send it by postal mail. And of course the cash system is not free, the costs are not paid directly by you.

I think there is some mistake in the question. It should be transaction fee instead of mining fee. i (exchange) is holding your $$$money. If you want to withdraw, I reserved the right to charge you a fee. Take it or leave it. Let said you are the exchange, will you do it for free instead and risk the responsibility of theft. it works both way.

exchange normally batch their transactions, I (exchange) don;t want to spend time for customer services (respond) by low-balling on transaction fees. When exchange batch a transaction, by right it should be confirmed quickly. Otherwise, mail-box will be full. The question is how much extra the exchange charged from their actual cost.

If you have given the private keys to the exchange, then the coins do not belong to you, do they? So when you move them to another exchange, they will change owners to the new exchange (i.e. new keys) and that involves the transaction being placed in a block which requires confirmation (or mining).

This is why it is never a good idea to keep bitcoin on an exchange, they are not really yours. Use your own hardware wallet. Or at least a wallet on your computer...

If you use BTC for smaller purchases then read up about the Lightning Network. I made a purchase yesterday for $100 and paid 0.001c in fees, which is negligible.