Medium's reading experience is pretty bad with all the annoying popups showing up all over the place. Also with Ghost you can easily export your data and move it across different ghost installations, you can customize the look and feel of the blog, you can use your own custom domain without paying medium extra for that, etc.

Medium has tracking and social media integration. And you don't have any real control over the platform.

(Also, the sticky headers are so damn annoying!)

Not giving your content to someone else. Not obeying their rules. Having control over the domain name (Medium doesn't support adding custom domains anymore).

medium is horrible if you want comments since it requires people to have medium account

also medium isn't nearly as customizable as your own blog. Can you do this on medium?

http://cabbibo.com/

medium doesn't allow you to bring your own domain, and that's fairly crucial. Both for longevity (can always point a domain at a new host, even if it's just a bunch of static files somewhere, if the old host goes away or becomes bad in some way) and identity: proper name instead of "yet another medium blog", which isn't exactly a signal of quality.

Still, there's tons of hosting options where that's not an issue. Running a VPS can be interesting and fun, but if you just want to host a simple site there's easier options that work just as well.