> To put it bluntly, I don't understand the tone of entitlement people have when they demand FB/Twitter/etc fix their individual problems.

Individual problems caused by the platform. If something or someone is causing a problem for me one method to rectify it is to simply ask them to help. It's a pretty standard thing in society.

> What I don't understand is why they think they have a right to demand that a platform they aren't even paying for should cater to them.

For the most part, they do have a right to demand the platform do whatever they want. And depending upon the request, the platform has the right to say "no" to those. The users then have the right to continue using the platform or not.