Outside of the digital world the equivalent is asking why buy a car vs renting one week to week.
Unless you trust the person who controls your server, your putting yourself in quite the position.
Social sites use your content to promote visitors to increase their value by volume and users.
The whole point of running forums yourself is to manage data from users at a place you call home sometimes using social networks to promote the rich content of your site.
The difference is night and day. One is filling in the blanks, the other is creating life.
I have several "tiny" forums. They are all public service. I have the server and get to choose entirely what is allowed on my sites. If someone or something doesn't suit my standards, it is gone. My forum, my rules.
1. Not having my own data backup.
2. Not being 100% sure that I could export all of my hard work.
3. Not being able to make easy use of exports of proprietary forums and software.
4. Lack of control over the quality of the site and downtime issues.
6. I can usually do a ton more with my own site than using someone else's premade tools that also limit my creativity.