Okay, Facebook right now has a complex problem statement. They position Facebook as a tool to help people connect and share their life. This is really complex and as I mentioned, figure out the smaller problems that help you solve the bigger problem. Facebook has identified a lot of those and is massively huge to take on all or most of these small problems. I shall answer your question according to the history available online.
Harvard had a Facebook of their own when Mark Zuckerberg was studying there. His frustration was that “he could only search and look at people’s information on the university’s Facebook and not perform any sort of social interactions (liking, commenting etc.)”.
He identified multiple trigger points. Personally, he wanted to do a social study and see what people thought about a particular set of images/paintings selected for study when the idea struck him.
His objective was to create a platform where members can search for people according to their interests and can create an online network of friends/study groups.
In fact if your objective is to start any form of social network, the common frustration comes from the lack of social interaction among a group of people who share common interests/attributes. Now the social network can be online or offline depending on which users you want to target and many other variables.
The trigger is commonly an activity which requires people to come in together as a group of social responsible beings and conduct the activity, whatever it may be. For example: discussions, meetings, events, entertainment and leisure activities, launches, parties etc.