I don't think it's so much that decentralized systems are technically safer, but that the people who own and control the centralized ones have incentives to keep them unsafe (at least from themselves) whereas if each person runs its own server, the incentives are properly aligned for security.
In essence, it's an economic argument, not a technical one.
>whereas if each person runs its own server, the incentives are properly aligned for security.
I don't see how this is true at all. Most people don't care/know about security. See Wordpress. Many companies don't take security seriously, there are many open mongodb pointing to the outside world - HackingTeam, a team chockfull of blackhat hackers, was partially done in by sloppy authentication and passwordless databases.
Today, when people run their own server, it doesn't seem the incentives are properly aligned at all - and given that even blackhat shops don't even take the time to secure their own systems properly, the economic argument falls flat.
In essence, it's an economic argument, not a technical one.