Bitcoin was created as a trustless and censorship-resistant currency in which the holder has complete control over his funds. It gives people the ability to be their own bank and to transact directly with one another. Centralized exchanges, despite providing a valuable service, remove this control from their users.
“A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution.” Satoshi Nakamoto, Bitcoin whitepaper, 2008
Hacks, fractional reserve systems, or plain theft can lead to the loss of user funds as we’ve seen over and over again with centralized services like Mt. Gox, Cryptsy, and most recently Bitfinex, that have lost millions in user funds. Furthermore, centralized exchanges employ KYC/AML policies that, combined with the transparent nature of the blockchain, strip the user of his privacy, and may cause fungibility issues. Centralized exchanges may also be subject to order book manipulation by corrupt operators. Ironically, every problem that Bitcoin solves can be found in these exchanges.
There are however some alternatives that employ blockchain technology to allow users to exchange cryptocurrencies, and even fiat currencies among themselves without the need to trust a centralized third party service.