Why do most developers prefer using Google, Facebook, Twitter and some other famous site details as log in option? Do they feel these site cannot be hacked or are they trying to get over the pain of maintaining a system that will keep users' details?

I think you're overestimating the role of developers in this question. Most sites have a team dedicated to product decisions, and most often, developers are NOT on that team as well. Generally developers have some ability to push back, but in this case, I don't think most would care that much.

I know this might shock people, but there was a time that people trusted Google. Generally, people thought that Google's security was much better than the security that they could build in their own data warehouses. Your user data lives somewhere, right? The question is who do you trust? The data warehouse company that is known locally, or the international giant who has a reputation to protect Then we found out that Google is giving data out to the government, and now no one knows why we have passwords anymore. Security is a f*cking joke, if NSA can recover anyone's password at any time.

This is just a matter of speeding up registration on a custom coded site. There is a pretty good chance that most users have a Google/Facebook/Twitter account, so by providing an external login option you not only allow new users to register on your site faster, but also make sure that the user doesn't simply leave your site because he/she doesn't have the time or doesn't feel like filling in the account registration form.