It really depends on whether you consider Craft a platform, that you're willing to do some custom development on, or an off-the-shelf, finished product.
Even though I love Craft, I have to be honest. As an off-the-shelf product, and if the main goal of the project is building a social network, I think you're be better off choosing some other, more specialised, platform.
You can probably solve all the things you mention with Craft; user handling, posting content to different channels from the front-end, updating content with likes, updating users with followers, etc. But, you don't get any specific social network functionality "for free", you'll have to use the building blocks that exists in Craft to create this functionality.
But, if you're willing to do some custom plugin development, you could definitely use Craft as the platform. The plugin API is extremely powerful, and let's you build and integrate pretty much whatever you want into Craft.