Facebook doesn't have a responsive design because their goal is to load the site and all the apps that hook into the platform as fast as possible with the least amount of overhead as possible.

As a large application, it is too complex to make responsive. It will make bad UX. Instead of making large web application responsive., it is better to have mobile version of web or mobile app.

Due to management reasons. For such a complex structure it is easier to manage single mobile pages.

Because they want you to use the app, which comes along with permissions to access your data.

To be fair, one would think it would be a bit more complex than that. Think about how large their codebase is and how many different types of browsers and devices they support.

So does Twitter.