Why would I want to put my money into something "decentralized" when my bank does a fine job?
Cryptocurrencies are complicated and nonsensical at times. I have yet to see anything in this space that makes me actually think it's the future of anything. It's far too risky.
Because you trust that your money will still be in the bank, in full, when you want to withdraw it. People in Cyprus, Venezuela, and Zimbabwe don't have that trust because it's been broken by bailouts and hyperinflation.
As long as the economy doesn't hyperinflate, and the banks don't haircut your accounts, and the IRS doesn't freeze your funds, and the government doesn't use civil forfeiture to take your money because they suspect you could be involved in criminal activity, your money is safe.
Therefore, many people see holding cryptocurrency as a hedge against that type of stuff.
Centralized exchange: send your FBI to exchange's wallet -> exchange updates your balance in its database, i.e. postgres -> trade for NSA -> withdraw NSA, which causes the exchange to send you NSA tokens (if they have them) and update another record in its DB.
The problem is in "if they have them". While normal banks are FDIC insured and a run on the bank won't prevent them from giving you your money, crypto exchanges provide no such guarantees. If the money is stolen from the exchange, like in the case of the OP, then you are SOL. Basically, you have to trust the exchange as much as you trust your bank. And clearly one entity is way more trustworthy than another.
In the decentralized exchange case, instead of trusting an organization to keep money safe through operational processes and tight regulation, you trust a smart contract. Provided that the smart contract has no bugs, this pretty much eliminates the need to trust the exchange. You trust it just as much as you trust mathematics.
Hope my explanation is not too verbose and makes sense.
On Ethereum this ecosystem is much more developed, and you can choose between EtherDelta, IDEX, 0xProject and Radex.
These exchanges eliminate counterparty risk because you control your funds at all times. They essentially act as matchmakers between those creating buy/sell orders and those who fill them.