I'm argentinian and in 2001, banks converted all USD money in the argentinian accounts to argentinian pesos. A lot of people lost money, because the peso plummeted in value after that. With a central authority things like this can happen at any time.
Descentralization is good because you remove a central authority that can modify the economic policy in an arbitrary way, it can seize or reduce your funds for arbitrary reasons, etc.
If Bitcoin had a centralized authority that would mean the policies that were set in the beginning (e.g. the quantity of coins that will be created, the fact that is a deflationary currency) could change. The fact that Bitcoin is descentralized means that the policies can't change, actually if they change it would not be Bitcoin anymore, it would be a new currency.
So from the beginning you know the "rules" in Bitcoin and you know they are not going to change because an arbitrary authority decided to change it. You are protected against arbitrary change in economic policies.
Also, being descentralized, you can do whathever with your money and hipotetically nobody can take it from you. A central authority could take your funds because arbitrary reasons (e.g. a new tax, etc.).
Also, being descentralized means it's really hard for a government to "shut down" Bitcoin.